PSU means power supply
A DC-DC power supply is one made to run on DC power rather than your homes AC power. These come in a varity of flavors, some are unregulated like the PW-70 etc which arent really much use in a car environment because your cars electrical system drops and spikes when doing things like starting the engine, so u need a regulator like the ITPS (which sucks because it wont survive crank and might not work with the engine off) or the carnetix (which will survive crank).
The opus power supply (and Maestro's DIY power supply) is a regulated power supply so you can connect it straight to your cars electrical system without worrying about any regulation (these both survive crank)
startup and shutdown controllers do just that, startup and shutdown the computer, they wait for u to start the engine to start the computer, and shut down the computer when you turn your car off, the ITPS, carnetix, and OPUS all include shutdown controllers
an invertor gives you AC power from your cars electrics, so basically you can plug in any home appliance like a normal power supply or your fridge or whatever, depending on the invertor and the load it may or may not survive cranking, which i guess isnt a problem for a fridge, but it'll **** you off if your computer has to restart.
hope that cleared it up for you