Provocateur Pillow

In "provocateur," a word borrowed directly from French, one sees the English verb "provoke." Both "provoke" and "provocateur" derive from Latin provocare, meaning "to call forth." Why do we say "provocateur" for one who incites another to action, instead of simply "provoker"? Perhaps it's because of "agent provocateur," a term of French origin that literally means "provoking agent." Both "agent provocateur" and the shortened "provocateur" can refer to someone (such as an undercover police officer or a political operative) whose job is to incite people to break the law so that they can be arrested. A person who provokes trouble, causes dissension, or the like; agitator.