egghead vs intellect

egghead and intellect both are nouns.

Word	Noun	Adjective	Verb	Adverb
egghead	Yes	No	No	No
intellect	Yes	No	No	No

As nouns, intellect is a hypernym of egghead; that is, intellect is a word with a broader meaning than egghead:

Other hypernyms of egghead include intellectual.

egghead (noun)	intellect (noun)
an intellectual; a very studious and academic person	the capacity for rational thought or inference or discrimination
	knowledge and intellectual ability
	a person who uses the mind creatively