Great review Lani!
The quick and short of it:
PVD is a process of applying different coating. Just like CVD (Chemical Vapor Disposition), PLD (Pulse Laser Disposition) and vacuum metalizing.
DLC, CTiN, TiN, etc. are all the different types of coating. DLC, I believe there are about 7 variants, us stirckly Carbon that is arranged in different structures that yield different properties.
TiCN, has the addition of Titanium, great for wear resistance and hardness, but no good in high temperature applications. I had a friend the ordered a .50Cal Desert Eagle in the TICN finish because it sounded so cool! Man was he [censored] when it arrived! Yep it is pink!
TiN has less the Carbon of TiCN, so it is not as hard, but handles high operating temperatures much better. A lot of cutting tools are coated in TiN.