I suppose I could put "būzdaroso?" here interchangeably, right?
I am guessing that dohaerir is any kind of servant, whether free or not, whereas būzdar is specifically a slave.
Yes, you are correct. However, the course has up until now always accepted "slave" as a translation for "dohaeriros".
Correction: Buzdar, Dohaeriros
There are two words because buzdar(i) is a foreign word for slave/servant (it's from Astapori Valyrian not High Valyrian). You can tell it's a foreign word because the -ar(i) ending isn't native to High Valyrian.