Why do track bikes vary between events?
Regarding handlebar selection, aero bars are only allowed in the pursuit (individual and team) and time trial events (1km TT, etc). All the other track events are drop bars only.

Wheel selection is a little more dependent on the rider's preference, though this is regulated as well; dual discs wheels are allowed for track time trials (essentially the same events that allow aero bars), while a deep section front wheel is always allowed.