Imaam Abu Muhammad Al-Hasan b. `Alee b. Khalaf al-Barbahaaree (died 329H, rahimahullaah) stated in his Sharhus-Sunnah (point 39):
واعلم بأن الدنيا دار إيمان وإسلام وأمة محمد صلى الله عليه وسلم فيها مؤمنون مسلمون في أحكامهم ومواريثهم وذبائحهم والصلاة عليهم ولا نشهد لأحد بحقيقة الإيمان حتى يأتي بجميع شرائع الإسلام فإن قصر في شيء من ذلك كان ناقص الإيمان حتى يتوب واعلم أن إيمانه إلى الله تعالى تام الإيمان أو ناقص الإيمان إلا ما أظهر لك من تضييع شرائع الإسلام
Know that the World is the abode of Imaan and Islaam. And the Ummah of Muhammad (may the peace and salutations of Allaah be upon him) has within it Mu’minoon and Muslimoon as it relates to their [general] rulings, and the rules of inheritance, and their slaughtered meat, and the funeral prayer that is performed over them.
We do not bear witness for any one of them that he has the true [complete] Imaan until he performs all the legislated rites of Islaam. And if he falls short in any affair from the legislated rites of Islaam, then he is considered to be deficient in Imaan until he repents.
Know that the actual knowledge [of the level] of Imaan of a person is with Allaah, the Most High: Perfection of Imaan or deficiency of Imaan, except that which is made apparent to you of negligence in the performance of the rites of Islaam.
Explanation of Shaikh al-Fawzaan:
It-haaf al-Qaaree of Shaikh al-Fawzaan vol. 1, p. 264 onwards):
“Know that the World is the abode of Imaan and Islaam.”
Meaning that Islaam and Imaan are performed for this World which is the abode of actions. As for the Hereafter, then it is the abode of recompense. So Islaam and Imaan are in this World – so whoever dies upon other than Islaam and Imaan, then he is a disbeliever (a Kaafir) – and it will not benefit him on the Day of Resurrection if he testifies to what he disbelieved in and then believes – or if he wishes to be returned [back to the World] and requests that from his Lord in order that he may believe:
وَلَوْ تَرَىٰ إِذْ وُقِفُوا عَلَى النَّارِ فَقَالُوا يَا لَيْتَنَا نُرَدُّ وَلَا نُكَذِّبَ بِآيَاتِ رَبِّنَا وَنَكُونَ مِنَ الْمُؤْمِنِينَ
“If you could but see when they are made to stand before the Fire and will say, “Oh, would that we could be returned [to life on earth] and not deny the signs of our Lord and be among the believers.””
There is a difference between Islaam and Imaan because of the fact that the Religion is of three levels:
And this is just as is stated in the hadeeth of Jibreel – the most comprehensive of these levels being Islaam because Islaam is to submit apparently (al-istislaam). It is possible that such a person is a believer (mu’min) inwardly or he could be a hypocrite (munaafiq) who submits to Islaam apparently whilst being a disbeliever inwardly.
As for the title of Imaan then it is not used for a hypocrite at all. It is used for a believer who is complete in Imaan, and for a believer who is deficient in Imaan. And it is the case that when Islaam and Imaan are mentioned together [in a revealed text], then each term has its own specific meaning. In this case what is intended by Islaam is the outward performance of the rites, and what is intended by Imaan are the inward rites, just as occurs in the hadeeth of Jibreel, wherein the Messenger (salallaahu ‘alaihi wassallam) said:
الْإِسْلَامُ أَنْ تَشْهَدَ أَنْ لَا إِلَهَ إِلَّا اللَّهُ وَأَنَّ مُحَمَّدًا رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ وَتُقِيمَ الصَّلَاةَ وَتُؤْتِيَ الزَّكَاةَ وَتَصُومَ رَمَضَانَ وَتَحُجَّ الْبَيْتَ إِنْ اسْتَطَعْتَ إِلَيْهِ سَبِيلً
“Islaam is that you testify that none has to right to be worshipped except Allaah, and that Muhammad is the Messenger of Allaah; that you establish the Prayer; that you give the Zakaah; that you fast the month of Ramadaan; that you perform Hajj to the House [in Mecca].”
So these are the outward actions. Then Jibreel asked:
فَأَخْبِرْنِي عَنْ الْإِيمَانِ
“Tell me about Imaan?”
So the Messenger responded:
قَالَ أَنْ تُؤْمِنَ بِاللَّهِ وَمَلَائِكَتِهِ وَكُتُبِهِ وَرُسُلِهِ وَالْيَوْمِ الْآخِرِ وَتُؤْمِنَ بِالْقَدَرِ خَيْرِهِ وَشَرِّهِ
“It is that you believe in Allaah, His Angels, His Books, His Messengers, the Last Day, and that you believe in the Pre-Decree, its good and evil.” 
So these are the inward, hidden actions.
( Reported by Muslim, no.1 from Umar Ibn al-Khattaab (radiyallaahu ‘anhu))
It is necessary for a person to combine between both Islaam and Imaan. If one finds in the revealed texts that only one of two is mentioned to the exclusion of the other, then the other is also intended. So if only the term Imaan is mentioned, then Islaam is also intended. And if only the term Islaam is mentioned, then Imaan is also intended. For this reason, the Scholars say: “If Islaam and Imaan are mentioned together, then each has a separate meaning. And if one is mentioned to the exclusion of the other, then it includes the meaning of the other.” Likewise is the case with the term al-faqeer (the person who poverty-stricken and destitute) and al-miskeen (the person who is poor and needy). If these two terms are mentioned together, then each one has its own separate definition, however if either one is mentioned to the exclusion of the other, then by necessity it includes the meaning of the other. 
( See Majmoo’ al-Fataawa 7/551)
The saying of Imaam al-Barbahaaree (d. 329H):
“And the Ummah of Muhammad (may the peace and salutations of Allaah be upon him) has within it Mu’minoon and Muslimoon as it relates to their [general] rulings, and the rules of inheritance, and their slaughtered meat, and the funeral prayer that is performed over them.”
The Ummah (nation) of the Prophet Muhammad (salallaahu ‘alaihi wassallam) are the Muslims and Mu’mins (Believers) because whosoever is a Mu’min is also a Muslim. But, whoever is a Muslim could be a Mu’min or he could be a hypocrite (Munaafiq). However, the correct Islaam necessitates that there be along with it something of Imaan, even if it be small:
قَالَتِ الْأَعْرَابُ آمَنَّا ۖ قُل لَّمْ تُؤْمِنُوا وَلَٰكِن قُولُوا أَسْلَمْنَا
“The bedouins say, “We have believed.” Say, “You have not [yet] believed; but say [instead], ‘We have submitted..'”
The saying of al-Barbahaaree:
“..as it relates to their [general] rulings, and the rules of inheritance..”
The Muslim, even if it is a mere outward display of Islaam, takes the ruling of the Muslims and they take responsibility for him. If he dies, they give him the ritual bath, they shroud him, they prayer the Janaazah prayer over him, and they bury him in the graveyard of the Muslims. During his lifetime, they should love him and show him allegiance. They show mercy to one another and are brotherly with one another. This is the Ummah of Muhammad (salallaahu ‘alaihi wassallam):
مَثَلُ الْمُؤْمِنِينَ فِي تَوَادِّهِمْ وَتَرَاحُمِهِمْ وَتَعَاطُفِهِمْ مَثَلُ الْجَسَدِ إِذَا اشْتَكَى مِنْهُ عُضْوٌ تَدَاعَى لَهُ سَائِرُ الْجَسَدِ بِالسَّهَرِ وَالْحُمَّى
“The similitude of the believers in their mutual love, mercy and affection are like one body. When one part suffers or is afflicted, the whole body responds to it with wakefulness and fever.” 
( Bukhaaree, no. 5665. Muslim, no. 2586, from Nu’maan Ibn Basheer (radiyallaahu anhumaa))
Allaah’s Messenger (salallaahu alaihi wassallam) stated:
إِنَّ الْمُؤْمِنَ لِلْمُؤْمِنِ كَالْبُنْيَانِ يَشُدُّ بَعْضُهُ بَعْضًا وَشَبَّكَ أَصَابِعَهُ
“Indeed the believer to a believer is like a building, each part supporting the other.” Then he interlocked his fingers of both hands to illustrate the point.
(Bukkaaree, no. 467. Muslim, no. 2586)
So they are believers:
إِنَّمَا الْمُؤْمِنُونَ إِخْوَةٌ
“The believers are but brothers.”
They are brothers in Imaan, in faith, not in ancestry or lineage.
The author said:
“..and their slaughtered meat..”
The slaughtered meat of the Muslim is halaal (permissible), even if that Muslim be an open sinner. So long as he has not left the fold of Islaam, the meat he slaughters is halaal for the Muslims to eat. Likewise with the hypocrite, the meat he slaughters is halaal to eat for us under the ruling that he is a Muslim, so long as it has not become clear to us that he is a Munaafiq (hypocrite outside of Islaam). Allaah, the Most High, said:
إِلَّا مَا ذَكَّيْتُمْ
“..except what you [are able to] slaughter [before its death]..”
So this is an address to the Muslims. Allaah has also permitted for us the slaughtered meat of the People of the Book (the Jews and Christians). Allaah, the Most High, said:
وَطَعَامُ الَّذِينَ أُوتُوا الْكِتَابَ حِلٌّ لَّكُمْ
“..and the food (i.e. the slaughtered meat) of those who were given the Scripture is lawful for you..”
Meaning that their slaughtered meat is permitted because they slaughter upon the way of the Sharee’ah which is obligated upon them in the scripture that is with them.
As for the meat of the idol-worshippers, the disbelievers, the atheist evolutionists, and the apostates, then we do not eat it. This is because the slaughtered meat of the unbelievers is impure – it is considered as being dead [not slaughtered] and it is impure with unbelief, because it is affected by the one who slaughtered it so it becomes impure. Since Allaah, the Mighty and Majestic, has permitted for us the slaughtered meat of the People of the Book (the Jews and Christians) specifically, then it becomes a proof for the forbiddance of the meat of anyone other than them.
The statement of Imaam al-Barbahaaree:
“..and the funeral prayer that is performed over them..”
The prayer is prayed over every Muslim, even if he is an open sinner, or one who is disobedient, or a Munaafiq so long as his hypocrisy is not apparent and has not exited Islaam – then such a person is prayed over, and he is supplicated for, and forgiveness is sought for him, and his close Muslim relatives inherit from him, and he inherits from his close Muslim relatives.
Imaam al-Barbahaaree said:
“We do not bear witness for any one of them that he has the true [complete] Imaan until he performs all the legislated rites of Islaam.”
We do not praise anyone by saying: So-and-so is a Mu’min (Believer). This is because the testimony for him that he is believer may not apply to him. When a man came to the Prophet (salallaahu ‘alaihi wassallam) and said: “Give to so-and-so for indeed he is a Believer (Mu’min).” The Prophet (salallaahu ‘alaihi wassallam) corrected him by saying: “Or he is a Muslim.” The man said again: “Give to so-and-so for indeed he is a Believer.” The Prophet (salallaahu ‘alaihi wassallam) said: “Or a Muslim.” 
( Bukhaaree, no. 27. Muslim, no. 150, from Sa’d Ibn Abee Waqaas (radiyallaahu ‘anhu))
The Prophet intended by this that a person does not glorify another person, rather he gives him a general title by saying, “He is a Muslim.” So it may be the case that a Muslim is firmly established upon his Religion, or he may be a Muslim with sins, or he may be disobedient or deficient, or he may be a hypocrite – so you do not testify for him perfection.
Al-Barbahaaree (rahimhullaah) said:
“And if he falls short in any affair from the legislated rites of Islaam, then he is considered to be deficient in Imaan until he repents.”
The ‘Aqeedah (belief) of Ahlus-Sunnah wal-Jamaa’ah is that the sinner, if his sin is from the major sins, so long as it is not polytheism (shirk), then it does not exit him from Islaam, or it does not remove him from the circle of Imaan. Rather, he is a Mu’min (a believer) due to his Imaan, and a sinner due to his major sin. Or you would say: He is believer who is deficient in Imaan.
Imaam al-Barbahaaree (rahimahullaah) said:
“Know that the actual knowledge [of the level] of Imaan of a person is with Allaah, the Most High: The perfection of Imaan or deficiency of Imaan…”
Meaning that we accept from a person what is apparent and leave to Allaah what is hidden.
Imaam al-Barbahaaree said:
“..except that which is made apparent to you of negligence in the performance of the rites of Islaam.”
Meaning, except if he falls into a nullifier from the nullifiers of Islaam. From those nullifiers is to abandon the Islamic Legislations – then you would judge such a person with apostasy, such as if a person was to abandon the Salaah (Prayer) deliberately, or that he speaks with words of Kufr (disbelief) such as reviling Allaah, or reviling the Messenger (salallaahu ‘alaihi wassallam), or reviling the religion of Islaam. In such a situation, you would judge that person to have apostated.
Whoever makes manifest a nullifier from the nullifiers of Islaam, alongside removing from him the excuses (al-‘udhr), and removing the barriers (al-mawaani’), e.g:
- Does he have an [excusable] interpretation?
- Is he a Muqallid (a blind-follower of someone who has lead him astray)?
- Is he ignorant [ such that he has an excuse)?
- Was he angry [at the time he committed the kufr]?
Then the ruling of apostasy is not applied to him alongside these barriers.