I believe "Country/Western" was a label for radio stations, roughly depicting the range of music played. It's a fairly broad category. I see it going from the folky side of county (Appalachian ballads) through old Nashville stuff, Western Swing, to cowboy songs. (That was 30-60 years ago. What the "Country" stations play nowadays is mostly insipid pop ballads with a nasal twang and rock music with steel guitar thrown in--and no, I'm not at all opinionated about this [BG]). So I guess the answer to your question, KingB, is that Country is one part of the Country/Western category. As to where the lines are drawn, that could be tough to nail down.

I recall a discussion of this in some previous thread, and I think it was Catspaw who gave a clear and fairly thorough run-through of the genre(s).