The terms Muslim and Mu’min or Iman and Islam are sometimes used interchangeably or one is used with the intention that the other is included in the meaning. However, technically we make a distinction between them based on Qur’an and hadith.
قَالَتِ ٱلۡأَعۡرَابُ ءَامَنَّاۖ قُل لَّمۡ تُؤۡمِنُواْ وَلَـٰكِن قُولُوٓاْ أَسۡلَمۡنَا وَلَمَّا يَدۡخُلِ ٱلۡإِيمَـٰنُ فِى قُلُوبِكُمۡۖ
“The bedouins say, “We have believed.” Say, ‘You have not [yet] believed; but say [instead], ‘We have submitted,’ for faith has not yet entered your hearts…'” [Qur’an; 49:14]
Simply put, a Muslim is someone who has accepted the message of Islam, while a Mu’min is one who has faith in his heart. It is possible that a person may accept Islam and be a Muslim, but perhaps faith has not settled in his heart yet. On the contrary, when faith is present, it would most likely manifest in outward actions as well.
إِنَّمَا ٱلۡمُؤۡمِنُونَ ٱلَّذِينَ إِذَا ذُكِرَ ٱللَّهُ وَجِلَتۡ قُلُوبُہُمۡ وَإِذَا تُلِيَتۡ عَلَيۡہِمۡ ءَايَـٰتُهُ ۥ زَادَتۡہُمۡ إِيمَـٰنً۬ا وَعَلَىٰ رَبِّهِمۡ يَتَوَكَّلُونَ / ٱلَّذِينَ يُقِيمُونَ ٱلصَّلَوٰةَ وَمِمَّا رَزَقۡنَـٰهُمۡ يُنفِقُونَ / أُوْلَـٰٓٮِٕكَ هُمُ ٱلۡمُؤۡمِنُونَ حَقًّ۬اۚ لَّهُمۡ دَرَجَـٰتٌ عِندَ رَبِّهِمۡ وَمَغۡفِرَةٌ۬ وَرِزۡقٌ۬ ڪَرِيمٌ۬
“The believers are only those who, when Allah is mentioned, their hearts become fearful, and when His verses are recited to them, it increases them in faith; and upon their Lord they rely – The ones who establish prayer, and from what We have provided them, they spend. Those are the believers, truly. For them are degrees [of high position] with their Lord and forgiveness and noble provision.” [Qur’an; 8:2-4]
The famous hadith Jibreel elucidates these terms further:
On the authority of Umar (may Allah be pleased with him) who said, “While we were one day sitting with the Messenger of Allah (peace and blessings of Allah be upon him) there appeared before us a man dressed in extremely white clothes and with very black hair. No traces of journeying were visible on him, and none of us knew him.
He sat down close by the Prophet (peace and blessings of Allah be upon him), rested his knees against the knees of the Prophet (peace and blessings of Allah be upon him) and placed his palms over his thighs, and said, “O Muhammad! Inform me about Islam.”
The Messenger of Allah (peace and blessings of Allah be upon him) replied, “Islam is that you should testify that there is no deity worthy of worship except Allah and that Muhammad is His Messenger (peace and blessings of Allah be upon him), that you should perform salah (ritual prayer), pay the zakah, fast during Ramadan, and perform Hajj (pilgrimage) to the House (the Ka`bah at Makkah), if you can find a way to it (or find the means for making the journey to it).”
He said, “You have spoken the truth.” We were astonished at his thus questioning him (peace and blessings of Allah be upon him) and then telling him that he was right, but he went on to say, “Inform me about Iman (faith).”
He (the Prophet) answered, “It is that you believe in Allah and His angels and His Books and His Messengers and in the Last Day, and in fate (qadar), both in its good and in its evil aspects.”
He said, “You have spoken the truth.” Then he (the man) said, “Inform me about Ihsan.” He (the Prophet) answered, “It is that you should serve Allah as though you could see Him, for though you cannot see Him yet He sees you.”
He said, “Inform me about the Hour.” He (the Prophet) said, “About that the one questioned knows no more than the questioner.” So he said, “Well, inform me about its signs.” He said, “They are that the slave-girl will give birth to her mistress and that you will see the barefooted ones, the naked, the destitute, the herdsmen of the sheep (competing with each other) in raising lofty buildings.”
Thereupon the man went off. I waited a while, and then he (the Prophet) said, “O Umar, do you know who that questioner was?” I replied, “Allah and His Messenger know better.” He said, “That was Jibril. He came to teach you your religion.” [Muslim]
The Qur’an says:
يَـٰٓأَيُّہَا ٱلَّذِينَ ءَامَنُواْ ٱتَّقُواْ ٱللَّهَ حَقَّ تُقَاتِهِۦ وَلَا تَمُوتُنَّ إِلَّا وَأَنتُم مُّسۡلِمُونَ
“O you who have believed, fear Allah as He should be feared and do not die except as Muslims [in submission to Him].” [Qur’an; 3:102]