These aren't eye styles (shape-based) but types based on how they look.

I made an example of each I could remember.

An Angel eye : Hazael's, Camael's, Raphael's, Metatron's, etc...
It's grayish on the Iris borders, colored (blue, gree, yellow, etc) on it's core and the pupil is white.

A normal human eye: on the example I've used Isaack, is the basic one.
Darker/black pupil, colored iris.

God eye: Ghnin, Cella, Lumiann, etc... (except Skahi)
Clear and brighty colors on the iris, darker color on the border of the pupil, clearer color on the core.

Jenova Descendant eye: Sephiroth's, Seth's, Damian's.
Slit pupil.

Vampire eye: Leon's, Millia's, Rurik's, etc...
Brightless iris with usually pale colors (sometimes bright) pupil and iris of the same color with a slightly variation on the pupil border.

Drow and Shadow based eyes: Cynnah, Skahi, Lachesys, etc.
With some slight variation, but mainly with silver, gray, white Iris, black, gray or white slit pupil and black sclera.

These are the ones I can remember for now :3''

Hope you find it interesting...

D:' My arm still aches, so I can just doodle...