Peter has pretty much it the head on the nail.
BUF Tower indeed has a BRITE in the cab (actually they have 4, i believe).
There is a VFR pattern at all airports. Generally all turns are to the left. Downwind is parallel to the runway. Base is perpendicular from the runway (before you turn final). "Left" and "Right" are the terms used to designate which way they will turn (i.e. left turn or right turn).
Sometimes we'll get the pilots who call, "Heeeey, tower, jetlink 2267, 5 mile right base for 23."
"High downwind" is almost always for arrivals from the south and west that are brough north of the airport (between IAG and BUF) but are kept high because of some obstacles. So, they'll be at 6000, call the field, cleared for the visual, and then start down. So by the time they call the tower, there about 4000MSL (a little higher than 2000AGL, Peter).
The main things is, very few pilots know which towers have BRITEs and which don't. So they just give there position initially so (if we didn't have a BRITE) we wouldn't have to ask or look.
To make things easier, what i'll do when on an instrument approach is something like, "Tower N40060 KLUMP for 23." I'll reference myself to the outer marker. The airliners will some times do that too.