Ivy Leaguer vs grad

Ivy Leaguer and grad both are nouns.

Word	Noun	Adjective	Verb	Adverb
Ivy Leaguer	Yes	No	No	No
grad	Yes	No	No	No

As nouns, grad is a hypernym of Ivy Leaguer; that is, grad is a word with a broader meaning than Ivy Leaguer:

Ivy Leaguer: a graduate at an Ivy League school
grad: a person who has received a degree from a school (high school or college or university)

Other hypernyms of Ivy Leaguer include alum, graduate.

Ivy Leaguer (noun)	grad (noun)
a student at an Ivy League school	a person who has received a degree from a school (high school or college or university)
a graduate at an Ivy League school	one-hundredth of a right angle