proctor vs keep an eye on

proctor is a noun but keep an eye on is not a noun.

Word	Noun	Adjective	Verb	Adverb
proctor	Yes	No	Yes	No
keep an eye on	No	No	Yes	No

As verbs, keep an eye on is a hypernym of proctor; that is, keep an eye on is a word with a broader meaning than proctor:

Other hypernyms of proctor include follow, observe, watch, watch over.

proctor (noun)	keep an eye on (noun)
someone who supervises (an examination)

proctor (verb)	keep an eye on (verb)
watch over (students taking an exam, to prevent cheating)	follow with the eyes or the mind