The two words are synonyms. Just call them Muslims and be done with it.
Call them MOSLEMS! I took a photo 30 years ago while I was hanging off the back of an Embassy Van of a traffic sign in Saudi Arabia that ordered all non-MOSLEM drivers to exit. We had to get off on what we called the “Christian Bypass” lest we infidels enter the MOSLEM holy city of “Makkah.”