What is the word when a place is ruled by another country?

Depending on the context (also: historical time) of the situation, mutual agreement between the two places and the terms actually used in their legal documents, it could be:

a dependency

a colony

a territory (for example: Puerto Rico is an unincorporated US territory)

and some others: people in the past have used different words to mask the fact that they dominate another country against their will ...