cover vs make up

cover is a noun but make up is not a noun.

Word	Noun	Adjective	Verb	Adverb
cover	Yes	No	Yes	No
make up	No	No	Yes	No

As verbs, make up is a hypernym of cover; that is, make up is a word with a broader meaning than cover:

cover: make up for shortcomings or a feeling of inferiority by exaggerating good qualities
make up: adjust for

Other hypernyms of cover include compensate, correct, counterbalance, even off, even out, even up.

cover (noun)	make up (noun)
the act of concealing the existence of something by obstructing the view of it
fire that makes it difficult for the enemy to fire on your own individuals or formations
a false identity and background (especially one created for an undercover agent)
a recording of a song that was first recorded or made popular by somebody else
bedding that keeps a person warm in bed
a covering that serves to conceal or shelter something
covering for a hole (especially a hole in the top of a container)
the protective covering on the front, back, and spine of a book
a natural object that covers or envelops
a fixed charge by a restaurant or nightclub over and above the charge for food and drink

cover (verb)	make up (verb)
sit on (eggs)	apply make-up or cosmetics to one's face to appear prettier
clothe, as if for protection from the elements	put in order or neaten
protect by insurance	come to terms
act on verbally or in some form of artistic expression	concoct something artificial or untrue
be responsible for reporting the details of, as in journalism	devise or compose
maintain a check on; especially by patrolling	do or give something to somebody in return
protect or defend (a position in a game)	make up work that was missed due to absence at a later point
hold within range of an aimed firearm	form or compose
play a higher card than the one previously played	adjust for
be responsible for guarding an opponent in a game
provide with a covering or cause to be covered
form a cover over
copulate with a female, used especially of horses
cover as if with a shroud
put something on top of something else
travel across or pass over
hide from view or knowledge
spread over a surface to conceal or protect
be sufficient to meet, defray, or offset the charge or cost of
to take an action to protect against future problems
invest with a large or excessive amount of something
help out by taking someone's place and temporarily assuming his responsibilities
provide for
span an interval of distance, space or time
include in scope; include as part of something broader; have as one's sphere or territory
make up for shortcomings or a feeling of inferiority by exaggerating good qualities