Here are the basics....
(Aux) Sends, channel based signal send, which will send a signal to a discrete location, (commonly a TRS output jack on a mixer) it would be commonly sent to an fx processor such as reverb, delay or chorus as examples and the returning signal from the fx (often pseudo stereo in nature) would be brought back into a set of faders on the desk so the "return" signal can be mixed in. Or the signal could return to a dedicated "Auxiliary return" a stereo set of inputs which are routable to the master stereo bus. (and often other locations)
Bus, often stereo in nature and often used via routing buttons on near the fader of the mixer.
Often used for grouping signals of similar origin i.e. drums, synths, guitars. This allows control of level
of a "group" of signals on 1 (or a L/R pair) of faders, keeping the instruments relative balance.
Aux is usually an abrieviation of " Auxilary send" as explained above.
cheers