"a. A disk designed to be played on a phonograph."
"3. A vinyl disc on which sound is recorded and may be replayed on a phonograph. ex: I still like records better than CDs."
Vinyl doesn't always refer to a disc that has audio recordings etched into it, either. Both words have more than one meaning, but "record" means what I used it for, also.
Edit: I think it's funny that someone who has learned English as a foreign language is trying to correct an English teacher Not that I'm never wrong, but in most cases with English, I know damn well what I'm talking about. :-P