These words have a distinction that is not always drawn.
When dealing with percentages, "most" and "majority" mean "significantly more than half." They do not mean "the biggest group there is." If the biggest group makes up 87% of the whole, that's the "majority." If the biggest group makes up less than half, like 42% of the whole (and the other groups are, say, 18%, 23% and 17%), then that is the "plurality" -- the biggest group but not more than half. These distinctions are usually limited to discussions of relative values, especially votes in an election.
"There was no majority winner, but a plurality of votes were cast for the incumbent."
In other contexts, "plurality" can mean just "a large number of things," and "most" can mean "the biggest or most pronounced out of the group." (But "majority" retains its more-than-half/almost-all meaning at all times.)
"Gina showed the most improvement of any student in the class," does not have to mean that Gina showed more than half of all the class' collective improvement.