so my question is: What are considered the Chassis fans and what is the Power fan on my case?
All the fans of your chassis (case) are Chassis fans. Where you plug what fan into is of your own knowledge. You have 3 fans...plug 'em in as you see fit.
I have several versions of the P8Z77-V board, but not the LX. You shouldn't have a "PWR" header these days. That is meant for PSU's that needed/had externally regulated fans so we can control them from the MOBO settings in the BIOS. I haven't seen that in a very long time. But you can still connect a case fan to it if you have one and still control it from the BIOS. Just know it's not your PSU and is so-and-so fan you hooked it to.
Quickly, they're just labels and act no differently. When you hook a fan to one of them, you'll know what fan it is to tweak in the BIOS. The CPU, yeah it'll be different and speaks for itself.