Great question, Derek.

I would define a timber framer as "one who builds timber framed structures"

But for more specific meaning, I think it depends on which adjective you use.

Professional Timber Framer--a carpenter who earns their daily living practicing the trade of timber framing

Amateur Timber Framer--a person who is an enthusiast of the craft of timber framing and pursues it as a hobby

Itinerant Timber Framer--a professional timber framer who works independently on a freelance basis


Soon to exist:
Guild Apprentice Timber Framer
Licensed Journeyworker Timber Framer

These definitions are, of course, my .02.
Anyone have any others to add?
Whit