surface vs cover

surface and cover both are nouns.

Word	Noun	Adjective	Verb	Adverb
surface	Yes	Yes	Yes	No
cover	Yes	No	Yes	No

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

surface (noun)	cover (noun)
the outer boundary of an artifact or a material layer constituting or resembling such a boundary	the act of concealing the existence of something by obstructing the view of it
a device that provides reactive force when in motion relative to the surrounding air; can lift or control a plane in flight	fire that makes it difficult for the enemy to fire on your own individuals or formations
a superficial aspect as opposed to the real nature of something	a false identity and background (especially one created for an undercover agent)
information that has become public	a recording of a song that was first recorded or made popular by somebody else
the extended two-dimensional outer boundary of a three-dimensional object	bedding that keeps a person warm in bed
the outermost level of the land or sea	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

surface (adjective)	cover (adjective)
on the surface

surface (verb)	cover (verb)
appear or become visible; make a showing	sit on (eggs)
put a coat on; cover the surface of; furnish with a surface	clothe, as if for protection from the elements
come to the surface	protect by insurance
	act on verbally or in some form of artistic expression
	be responsible for reporting the details of, as in journalism
	maintain a check on; especially by patrolling
	protect or defend (a position in a game)
	hold within range of an aimed firearm
	play a higher card than the one previously played
	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