IMHO,
There is a thing called flyfishing. It is done with a hand-tied bug imitation of feathers and other assorted materials. It imitates a fly of some sort at some particular stage in it's life cycle. Thus the name.
A flyrod can be used for lots of other applications (and just as enjoyable). Casting light streamers, popping bugs, etc. i fall into this category of fisherman most often.
It's all fishing. And I'd much rather be doing it than working any day. I love catching bass and bream on wooly buggers with my fly rod. It's not technically flyfishing, but it sure is fun. I think of it as ultra-finesse fishing, and I have a great time doing it.
I also love catching fish on those little tiny flies.