question #1 Sahih Muslim 150a, Book 1, Hadith 285 : What is the distinction between a believer and a Muslim in the context of this narration?

The Messenger of Allah (ﷺ) distributed shares (of booty among his Companions). I said: Messenger of Allah! Give it to so and so, for verily he is a believer. Upon this the Messenger of Allah remarked: Or a Muslim. I (the narrator) repeated it (the word” believer” ) thrice and he (the Holy Prophet) turned his back upon me (and substituted the word)” Muslim,” and then observed: I bestow it (this share) to a man out of apprehension lest Allah should throw him prostrate into the fire (of Hell) whereas in fact the other man is dearer to me than he.