What is the difference between a missionary and a great prophet?

Solution 1:

Great Prophets are much more powerful (as their name would suggest). They can found and enhance religions, construct holy sites, and spread their religion 4 times. And when converting units, they can also remove existing religions from the city as well.

Missionaries can only spread religion, and they can only do so 2 times (3 if you have the Great Mosque of Djenne). Also, if you end your turn with a missionary in a rival's territory where you do not have an open borders treaty, they lose 25% of their maximum conversion power. If they lose all their power, they disappear (called attrition).

Both of these units can enter into another player's territory without starting a war, even if you don't have an open borders treaty with that country.