A Muslim is by definition one who submits his will to Allah and adheres to the principles of Allah’s religion. We therefore believe that all Prophets were by definition Muslim.

When his Lord said to him (Abraham), “Submit”, he said “I have submitted [in Islam] to the Lord of the worlds.” [Quran 2:131]

A Muslim is the one who accepts Allah as the One and Only God who is worthy of worship and that Muhammad (pbuh) is the last and Final Messenger.

There is also however a difference between a Muslim (One who submits) and a Mu’min (One who believes). As Allah states in the Quran:

“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. And if you obey Allah and His Messenger, He will not deprive you from your deeds of anything. Indeed, Allah is Forgiving and Merciful.” [Quran 49:14]

To attain the status of a true believer in Islam one must strive to attain true faith. This is exemplified through the Quran and many of the Hadith ( Narrations) of Muhammad (pbuh).

“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.” [Quran 8:2-4]
In the Hadith of Muhammad (pbuh) we also find

“”No one of you becomes a true believer until he likes for his brother what he likes for himself”. [Al-Bukhari and Muslim].

“The most perfect believer in faith is the one who is best in moral character. The best of you are those who are the best to their spouses in manners.” [Al-Tirmidhi 1082].

“A true Muslim is one from [the transgressions of whose tongue and hands, all other Muslims are safe; And a true Mu’min is one from whom people’s lives and wealth are secured;” [Al-Bukhari and Muslim].

“None of you will truly believe until I am more beloved to him than his father, his son and all of mankind.” [Al-Bukhari and Muslim].