In my head, "carpenter" just has a different connotation. But it's not very clear-cut. I used to DJ a lot at parties during my university years, was I "a DJ"? I prepare dinner for 8-10 guests regularly, am I "a cook"?
It kind of depends, I guess. I've drawn a large number of cartoons in my life, but (with few exceptions) never sold them for money. I wouldn't call myself a cartoonist (mainly because I don't do it as much recently), but I would definitely not call myself "not a cartoonist" :) That would be selling myself short :)
I'm not a programmer professionally either. But then, I do have a CS degree, and I still write code almost daily. I'm a programmer.
I also generally don't feel that the fact if you do something professionally (for money) should really count as "what you do" (identity, in a sense), as this comic illustrates: http://i.imgur.com/MNJzpqL.jpg (I didn't draw this, btw)