Correct, My understanding is that the term slave came from the Latin Sclāvus (“Slav”), because Slavs were so often forced into slavery. The Latin term is said to be rooted in Byzantine Greek usage.
Verginius is correct.
the endonym (i.e. self-term) for the Slavs is Slovianie meaning people who can speak (from Slowo, the word for, well, “word”). As an aside, the Slavic term for Germanic peoples is “Niemcy” or “mute-people” i.e. people who can’t speak. I find it hilarious to think of the early Slavs meeting the early Germanics and going “what the Czarnobog is this guy saying? He must be unable to speak” :)