Islām is the name of the religion, and a Muslim is a person who follows that religion. They don't both mean the same thing. Also, in Arabic, the two words are not very different, but in fact are related - both contain the three-consonant root "s-l-m" as you can see in Islām and Muslim. Words containing those consonants in that order all will have similar meanings in Arabic - in this case, the basic meaning is "peace," (as with another well-known Arabic word, "salām") and this particular form comes from the verb "aslama", meaning "to submit", i.e. to the will of God. "Islām" is the noun formed from that verb ("submission"), and "Muslim" is the conjugation meaning someone who performs the action of the verb ("submitter").

So, the two words actually are directly related, just not in a way which would be obvious to a non-Arabic speaker.