support vs back up

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

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

As verbs, back up is a hyponym of support; that is, back up is a word with a more specific, narrower meaning than support:

Other hyponyms of support include back, vouch, verify, demonstrate, establish, prove, shew, show, document, validate.

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

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

support (noun)	back up (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

support (verb)	back up (verb)
establish or strengthen as with new evidence or facts	establish as valid or genuine
put up with something or somebody unpleasant	become or cause to become obstructed
adopt as a belief	make a copy of (a computer file) especially for storage in another place as a security copy
argue or speak in defense of	move backwards from a certain position
be a regular customer or client of	give moral or psychological support, aid, or courage to
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