Joel-
Basically, a summing mixer and regular mixer do the same thing. 'Regular' mixers would be those that have faders, aux sends, group outputs, etc., which you would need to construct a mix. Summing mixers have risen to prominence of late as many engineers hate the way a DAW mix bus sounds. These usually have a number of inputs that just sum to a main stereo output, as they will use the DAW's internal faders, aux sends, etc., to build the mix and feed the individual outputs. These outputs are then summed externally via the summing mixer to produce the main stereo mix and thus bypass the DAW's crappy(my own opinion, yours may vary) internal summing math. They also usually have only rudimentary panning options(Left/Right or L/C/R). Bare bones, which is really all you need in that scenario.
'Bus compressor' is really just another way of saying stereo compressor. Many old consoles had two or more compressors mounted in the console itself. For example, older Neves would have a pair of 2254's, and later ones would have 2-6 2264's or 32264's mounted in the meter bridge. Usually an engineer(if so inclined) would say "stick those across the mix bus". SSL's have a separate dedicated mix bus compressor in the center section meant exclusively for the mix bus. These eventually just came to be known as the 'bus compressor'. So while any stereo compressor can be a bus compressor, often times the reference to a bus compressor means something high end like a Neve or SSL.
Sorry for being so long-winded.
Zach