Unlike the absolute rule of a sovereign over his local nation or of an emperor over the divisions of his empire, a suzernation exercised control over a smaller or weaker nation in international affairs, while allowing a large measure of independence on the domestic level.
Usually, the contract or suzerainty treaty he offered his subjugated neighbor was quite advantageous, both economically and in regard to military security.
(The Origin of the Bible: Newly Updated by F. F. Bruce, J. I. Packer, Philip W. Comfort, and Carl F. H. Henry, 2020. Literature in Bible Times by Milton C. Fisher, Page 99-100.)