back up vs support

back up is not a noun while support is a noun.

Word	Noun	Adjective	Verb	Adverb
back up	No	No	Yes	No
support	Yes	No	Yes	No

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

Other hypernyms of back up include affirm, confirm, corroborate, substantiate, sustain.

As verbs, back up and support are synonyms defined as:

back up and support: give moral or psychological support, aid, or courage to

back up (noun)	support (noun)
	aiding the cause or policy or interests of
	the act of bearing the weight of or strengthening
	documentary validation
	a military operation (often involving new supplies of men and materiel) to strengthen a military force or aid in the performance of its mission
	the activity of providing for or maintaining by supplying with money or necessities
	any device that bears the weight of another thing
	supporting structure that holds up or provides a foundation
	something providing immaterial assistance to a person or cause or interest
	a musical part (vocal or instrumental) that supports or provides background for other musical parts
	the financial means whereby one lives
	financial resources provided to make some project possible

back up (verb)	support (verb)
establish as valid or genuine	establish or strengthen as with new evidence or facts
become or cause to become obstructed	put up with something or somebody unpleasant
make a copy of (a computer file) especially for storage in another place as a security copy	adopt as a belief
move backwards from a certain position	argue or speak in defense of
give moral or psychological support, aid, or courage to	be a regular customer or client of
	be the physical support of; carry the weight of
	play a subordinate role to (another performer)
	support materially or financially
	give moral or psychological support, aid, or courage to
	be behind; approve of
	support with evidence or authority or make more certain or confirm