Nymphs are the adolescent stage of life for mayflies, caddisflies, and stoneflies. Most if not all of this stage is spent either near the bottom of the water column or under rocks and burried in the stream bed. There is a twice daily phenom called behavioral drift that occurs usually near dawn and dusk where nymphs drift freely to redistribute themselves in the water course.
To fish nymphs try to keep your fly near or on the bottom of the stream.
Wet flies can immitate several phases of life from emerging mayflies, caddisflies, etc to drowned adults or spinners.
It is best to immitate these phases during an active period of emergence or during a spinner fall when there are like insects up in the water column. Sometimes they are swimming up, swimming down (caddis egg laying) or dead drifting.
I believe it is safe to call any fly fished in the middle column a wet fly while nymphs are relegated to the bottom and emergers to the surface, in the surface film or just below.
In the old days streamers were called wets because they got, um...well, wet. Some of the traditional streamers or wet flies immitated baitfish and crayfish and were very elaborately tied, similar to and some of the traditional salmon flies of old.
But I believe today we are talking about "wets" we mean leadwing coachmen, partridge & orange, green, yellow. and the like, both soft hackled and winged wets.
HTH,
Maurice