postgraduate vs grad student

postgraduate and grad student both are nouns.

Word	Noun	Adjective	Verb	Adverb
postgraduate	Yes	Yes	No	No
grad student	Yes	No	No	No

As nouns, postgraduate and grad student are synonyms defined as:

postgraduate and grad student: a student who continues studies after graduation

Other synonyms of postgraduate include graduate student.

postgraduate (noun)	grad student (noun)
a student who continues studies after graduation	a student who continues studies after graduation

postgraduate (adjective)	grad student (adjective)
of or relating to studies beyond a bachelor's degree