what's the difference between a monarch and a president?

The difference between the two is a monarch is ruler of monarchy or the head of state of a constitutional monarchy, while a president is the head of state of a republic or a representative democracy.

A monarch may reign for life or until abdication. In choosing the next monarch, hereditary succession within one patrilineal family has been common.

A president can only be in his position depending on the term length/limits on his country. In choosing the next president, election is held and the one with the majority will be the president.