I have read both your letters on conversion.  [1] [2] Can you explain to me what is the significance of the word "believers"?
How is Mu'min different from Muslim?

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Answer

The terms used for believers are Mu’min (pl. Mu’minun) and Muslim (pl. Muslimun). The difference expressed in these two words is explained in the Hadith given by Sahih Muslim (where it is recorded by Umar as having been taught by Muhammad,) that a Mu’min is one who has iman (faith). Faith being a sincere belief in God, His Angels, His inspired books, His prophets, the Day of Resurrection, and the predestination of good and evil; and that a Muslim is one who is resigned and obedient to the will of God, and bears witness that there is no God but God, and that Muhammad is His Apostle and is steadfast in prayer, and gives Zakat, or‘legal alms,’ and fasts in the month of Ramadan, and makes a pilgrimage to Mecca if he/she has the means.

The rewards in store for the believer are as follows:

Lo! those who say: Our Lord is Allah, and afterward are upright, the angels descend upon them, saying: Fear not nor grieve, but hear good tidings of the paradise which ye are promised. [Qur'an 41:130]

If any do deeds of righteousness,- be they male or female - and have faith, they will enter Heaven, and not the least injustice will be done to them. [Qur'an 4:21]