An interesting narration explaining the difference between a Muslim (one who has Islam) and Mumin (one who has Faith).
H 1499, CH 12, h 1
Muhammad ibn Yahya has narrated Ahmad ibn Muhammad from al-Hassan ibn Mahbub from Jamil ibn Salih from Sama’a who has said the following: “I requested abu ‘Abd Allah AS, ‘Teach me about Islam and belief. Are they different?’ He said, ‘Belief is inclusive of Islam but Islam is not inclusive of belief.’ I then asked, ‘Please describe them to me.’ He said, ‘Islam is to testify that no one deserves to be worshipped except Allah and to affirm the truthfulness of the Messenger of Allah. With it lives are protected, marriages and inheritance become lawful and a group of people acknowledge this much. Belief is guidance and that which forms in the heart of the qualities of Islam and that which takes form from its practice. Belief is a degree higher than Islam. Belief is inclusive of Islam in appearance but Islam is not inclusive of belief esoterically even though they may both apply to words and in description.’”
H 1493, CH 11, h 1 Ali ibn Ibrahim has narrated from his father from ibn abu ’Umayr from al- Hakam ibn Ayman from al-Qasim al-Sayrafi associate of al-Mufaddal who has said the following: “I heard abu ‘Abd Allah, AS, saying, ‘Islam is to spare lives, protect the trust and make the marriage lawful, but reward comes from faith and belief.’”