Short answer
Islam is the religion, and a Muslim is a person who follows it. In Arabic, Islam means submission to God and a Muslim means one who submits.
The fuller answer
The two words come from the same root, s-l-m, which also gives the word salam, peace. Because of this, Muslims say that Islam means finding peace through submitting to God's will, and the greeting between Muslims is 'peace be upon you'.
It is better to say 'Muslim' and not 'Mohammedan' for a follower. Muslims do not follow Muhammad ﷺ as a god or the founder of a new religion. They follow God, and Muhammad ﷺ was His final messenger.
This answer follows the mainstream Sunni understanding and is general learning, not a fatwa. Where Muslims differ, the answer says so. Have a question of your own? Write to us.