Suzerainty

Suzerainty (American accent: soo-zer-en-tee) happens when a country X has its own government but cannot act independently because of a more powerful country Y. This more powerful country Y is called the suzerain and can usually control the foreign relations of X (how X interacts with other countries).
It differs from sovereignty in that the tributary still has limited control of its own stuff and internal country affairs.
A suzerain can also mean a feudal lord. Vassals must pay tribute to the feudal lord.
Some examples.
The term suzerainty originally described the relationship between the Ottoman Empire and its surrounding regions including:
China historically had suzerainty over Mongolia, Korea.