What is the medical term for eye specialist?

Ocular
Orbit is the medical term for the eyeball.
I believe it's called Globe and can be divided into two segments, anterior and posterior.

Oculus. (pl. oculi).

Oculus sinister (left eye.)

Oculus dexter (right eye.)

The original answer is partially correct. The eye itself is made up of many, many parts and most MDs simply refer to it as an "eye".