Moslem is an alternate spelling of Muslim. The words have the same meanings in all contexts, and both spellings have been in use for several centuries.
Moslem was the preferred spelling until the first half of the 20th century. Today, Muslim is the preferred spelling.
According to Yii-Ann Christine Chen, “whereas for most English speakers, the two words are synonymous in meaning, the Arabic roots of the two words are very different. A Muslim in Arabic means “one who gives himself to God,” and is by definition, someone who adheres to Islam. By contrast, a Moslem in Arabic means “one who is evil and unjust” when the word is pronounced, as it is in English, Mozlem with a z.”
Chen also notes the word “Moslem” is still used by some institutions that have had long associations with it being part of their name. As examples she cites, The American Moslem Foundation and the academic journal, The Moslem World.