old boy vs grad

old boy and grad both are nouns.

Word	Noun	Adjective	Verb	Adverb
old boy	Yes	No	No	No
grad	Yes	No	No	No

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

old boy: a former male pupil of a school
grad: a person who has received a degree from a school (high school or college or university)

Other hypernyms of old boy include alum, graduate.

old boy (noun)	grad (noun)
a vivacious elderly man	a person who has received a degree from a school (high school or college or university)
a former male pupil of a school	one-hundredth of a right angle
a familiar term of address for a man