I think "curly" is kind of a more generic term. Out there in the regular world (where people don't have complex classification systems for their hair type), people will use the word curly pretty loosely.
KinkyKeeper is also onto something with her comments about the shape of curls/waves. I consider myself a wavy, but I'm not sure I have a single s-curve on my head. They're spirals -- just very, very loose and stretched out spirals. And yes, I describe them as curls at times -- even though they may not "technically" qualify.
It's another problem with the hairtyping systems we have, and with semantics. But I think it's unlikely that anybody using those terms is trying to steal anybody's anything.
Wurly and proud!
Modified CG since 2008.