I'm very familiar with car/truck electronics but what are tank electronics called and there purpose..

Most of the tank electronics will have their own naming system. Pretty much just identifying the models. Ours are currently just motherboards atm until we release the new one Tamiya as well has a naming system for their tank electronics such as DMD-XX or similar (I'm sure a Tamiya guy will step in and clarify the model numbers).
Aftermarket systems such as the IBU2, Clark, BARC (from YHR here on the forums), ElMod and similar will all have different naming schemes. The purpose of the tank controllers is to handle things like:
-independent track control
-turret rotation (or traverse if the tank is equipped)
-elevation
-recoil (if equipped)
-airsoft (if equipped)
-sound system
-smoke unit (if installed/equipped)
-lighting (headlights, tail lights, warning lights, etc.)
-infrared battle system (if equipped)

I'm sure there is something I forgot in there, but that is what most controllers need to handle. Some are specialized more towards the IR crowd, some are focused more towards sounds, some have PC interfaces to make things simpler, etc. Each has its own pros and cons. The boards I mentioned all have a vendor presence here on the forums except Tamiya, but there are plenty of guys here to help with those questions if needed too. Anything specific you want to ask about them?

Do the mother boards have receivers built in ? So basically the motherboard is an esc or electronic speed control with more functions. So I'm guessing that ir systems only work with the same motherboard.

Some do, like our system and the Heng Long system. Others will have external receivers.
Pretty much the motherboards are a bunch of ESCs if you want to think of it that way. Some systems (I believe elevation is handled via servo) will use different connections but brushed motors run the main tracks, turret rotation, and airsoft firing if you have an airsoft tank. IR systems are not interchangeable at this time. Brand vs Brand is good, but to do multiple systems you will need something like MAKO2 from RCTA or you will need to swap to that motherboard (or compatible brand) to do IR battles. Some tank clubs also have standards and rules as well.