Well, I will take exception to Pad's definition of a "run".
A run, as in a waterway, is just a small waterway. I don't know how many little headwater streams are called ____ Run, and there's no larger waterbody at the top, just little springs.
But in this context, a run is not a stream at all, it's a feature in a stream. A narrow deep area with current, a "channel". It can be between 2 large rocks, or an area gouged out up against a bank, etc. One of my favorite areas to nymph.
My personal definitions of common terms (other than "run").
Riffle: Area of wider, shallower, and faster water between pools, surface usually has a rippled appearance. That is the classic "riffle". But its often taken just to mean any faster current area, and thus it is an all-encompassing term which includes pocket water, runs, rapids, chutes, etc.
Pool: An area where the stream slows. The classic pool is also deep. But like riffle, it's an all-encompassing term which just means an area where the entire stream slows, so it can include holes, flats, etc.
Hole: Deep area
Head: The top of a pool, where the current dumps in.
Tailout: Bottom of pool, where the pool gets shallower and speeds up into the riffle.
Slack: Nearly zero current. Can be anywhere, but often taken to mean the "edge water" along the banks.
Pocket water: Fast areas, with lots of deep "pockets", big rocks, and other variations. The area behind a large boulder in the current is a "pocket."
Flat: Slow, wide, and shallow, typically poor trout water.
Seam: Dividing line betwen 2 different currents of different speeds. Good holding water. Often identifyable with "bubble lines."
Current break: Similar to seam, but usually one area is MUCH slower than the other. Obstructions like boulders and wingdams usually create a current break behind them, where the slack water meets the current. Heads of pools often have a current break too. Almost all eddy's have a current break where they meet the main current. Excellent ambush points for trout.
Glide: Area of moderate, constant current over a constant bottom, surface is smooth. Can be fairly deep.
Eddy: An area, due to obstructions and current breaks, which exhibits circular or upstream flow. Strong ones can be called a whirlpool.
Plunge Pool: Occurs with waterfalls and such, where downward force of water scours out the bottom and creates a deep area.
Rapid: Very heavy, turbulent flow.
Buffer: Area just upstream of an obstruction like a boulder, where the water "stacks up" before going around.
Pothole: Self-explanatory, usually formed in a hard bottom where a piece is removed. Very small deep area.
Chute: Narrow, extended heavy current area. Usually shallower and longer than a "run". Often occurs alongside cliff walls. Very common, for instance, in the Erie steelhead streams.
Shoal/Sandbar - midstream shallow area where sediment collects.
Wingdam - can be manmade or natural, but a dam jutting a distance out into the water but not wholely across the stream. Narrows the channel and creates a current break.
Microcurrent - Usually in moderate flow area. Region exhibits multiple and varying currents, creating a number of small seams. Can be very difficult to get drag free drifts.
Weedbeds - self explanatory, but usually contains a lot of food and creates a lot of microcurrents.
Gradient - term used for the vertical fall of a stream. High gradient means it falls fast.
Cascade - A succession of small waterfalls or rapids interrupted by plunge pools.
Riffle/pool ratio - self explanatory. Some streams have long riffles and short pools. Some have long pools and short riffles. This term is a measure of how much area of riffle there is compared to area of pool there is.
Channel - just means the main current flow of the stream. Does not include edge water or small side flows around islands, etc. In low water, the channel is often all that holds water.