|—||Bukhari and Muslim|
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. But if you obey Allah and His Messenger, He will not deprive you from your deeds of anything. Indeed, Allah is Forgiving and Merciful.” - 49:14
In this passage the Qur’an makes a distinction in states of being someone who surrenders his or her will to God (muslim) and someone who also has complete faith and trust in God. (mu’min pl. mu’mineen) A Muslim can practice all the outward motions of prayer, good works, and whatever else is divinely enjoined, while at the same time have some doubt about faith in his or her heart. Yet, a higher state of being is to be a mu’min - someone who has complete faith, trust, and certainty in the heart and who also surrenders his or her whole being to God. In terms of states of being, a muslim cannot be a mu’min, whereas a mu’min is necessarily also a muslim. It can be understood in terms of an upward motion, with muslim being the essential foundation and mu’min being the next level or state.
(from The Qur’an and Sayings of the Prophet Muhammad: Selections Annotated & Explained)