student vs tutee

student and tutee both are nouns.

Word	Noun	Adjective	Verb	Adverb
student	Yes	No	No	No
tutee	Yes	No	No	No

As nouns, tutee is a hyponym of student; that is, tutee 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
tutee: learns from a tutor

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

student (noun)	tutee (noun)
a learner who is enrolled in an educational institution	learns from a tutor
someone (especially a child) who learns (as from a teacher) or takes up knowledge or beliefs