PSG (polysomnography) - where they determine IF you have sleep apnea. You will usually have EKG, flow sensor (like wearing oxygen to your nose), pulse oximeter (little sensor on your finger, EEG (checking what stage of sleep you are in) and belly band (to measure diaphragm movement.
Titratrion - where they treat your apneas/hypopneas. Usually starting with a very low pressure until you get to sleep and then slowly turning up the pressure until all or most of the apneas/hypopneas go away. (pnea = breathing, "a" = without, apnea = without breathing, "hypo" = beneath/below, hypopnea = below normal or shallow breathing)
If you meet the criteria (demonstrate a high enough AHI/desats/etc) , they can do a "split-night" study and jump straight to the titration so you can get both part done in one night.