Parts of an X-ray machine

This website illustrates the process by which x-rays work, and gives some terminology for you. I think the diagrams really help with clarity too: http://www.latticesemi.com/solutions/marketsolutions/medical/digitalxraymachinecameras.cfm

I think the swiveling screen thingy you're referring to is the x-ray tube, which generates the x-rays.

Here's another link where you can buy parts. I'm not a radiologist so I'm not sure if this is the terminology you want or not, but it's more info either way: http://www.ashaindustries.com/index.html

Since you are talking about a terminal to view images, I'm assuming you are looking at digital radiography. The terminal is simply that...a terminal or monitor

The swiveling screen thingy? Not sure what you're referring to there. It probably is the tube housing (or camera). If you have an actual screen attached to the housing where you can view in real-time, it's a fluoroscope.

G,
I think your thingy is the collimator.
I'm picturing you looking at a ceiling mounted unit or a fixed stand and wanting to dial in the shot. You're using the knobs on the colimator.