A usurpation is when the ruler of a political entity (state, country, region, city, organisation, whatever) is forcefully replaced by a different ruler from within. But there is no change to the sovereignty of the entity. It's the same entity with the same borders and the same political status under new management. This usually happens from the inside (although external support can of course also help). The term is mostly used historically, though. Nowadays an event like that would be referred to as a "coup" or "putsch".
A conquest, on the other hand, was an event where one political entity forcefully took over another political entity through an offensive war. A successful conquest resulted in the conquered entity losing its sovereignty. Either in form of a subjugation, where it officially stayed intact but unofficially became a non-sovereign puppet subservient to the conquering entity. Or in form of an annexation, where the conquered territories became a part of the conquering entity. For example, in World War II, Nazi Germany subjugated France but annexed Czech.
Throughout history, subjugations or annexations often meant that the conquerors would replace the leadership of the conquered entity, but that does not necessarily need to happen. When the conquerors believe that the conquered leadership will now be loyal to them, then it is very well possible that they leave them in power in order to ensure a smooth transition to the new status quo.
Note that the concept of "right of conquest" is officially no longer a thing in international law. The international community is reluctant nowadays to recognize claims legitimized solely by force.