student vs quick study

student and quick study both are nouns.

Word	Noun	Adjective	Verb	Adverb
student	Yes	No	No	No
quick study	Yes	No	No	No

As nouns, quick study is a hyponym of student; that is, quick study is a word with a more specific, narrower meaning than student:

student: someone (especially a child) who learns (as from a teacher) or takes up knowledge or beliefs
quick study: someone able to acquire new knowledge and skills rapidly and easily

Other hyponyms of student include memoriser, memorizer, sponge, dweeb, grind, nerd, swot, wonk, tutee.

student (noun)	quick study (noun)
a learner who is enrolled in an educational institution	someone able to acquire new knowledge and skills rapidly and easily
someone (especially a child) who learns (as from a teacher) or takes up knowledge or beliefs