HID vs Halogen: Bulb or Assembly?

Long story. About 2 years ago I replaced the ballasts and headlights in my 2007. They were these ones and they worked great until I wrecked the car about a year ago. The shop I took the car into to fix bought a headlight from an old Prius, so it cost 500 to freaking replace. That was whatever I needed a car and didn't ask questions. Then about 2 weeks ago my headlight went out. I took the headlight out to see if I just needed a new bulb and there I find the exact wiring I had in the other headlight, in this one... I was pretty upset. This guy is gonna refund my money and I'm gonna just buy an aftermarket HID headlight, BUT my question is, what is the difference between the HID TYPE and the Halogen TYPE headlight assembly? Is it just the bulb that goes with them? Because I found a pair of Halogen TYPE headlights that come with HID bulbs, and I would like to put them in just so both sides match. Or can I buy a halogen TYPE assembly and put another HID kit in it? Or do I need to buy the HID type assembly?

I know that's a lot, but I really appreciate any help I can get. I'm going to call Toyota and see if they can explain it to me, but I kinda trust PC guys more than Toyota people haha.

I guess basically what I'm asking is will the Halogen Type Assembly fit in an HID Prius? Or are the dimensions different?