influence vs support

influence and support both are nouns.

Word	Noun	Adjective	Verb	Adverb
influence	Yes	No	Yes	No
support	Yes	No	Yes	No

As nouns, support is a hyponym of influence; that is, support is a word with a more specific, narrower meaning than influence:

influence: a cognitive factor that tends to have an effect on what you do
support: something providing immaterial assistance to a person or cause or interest

Other hyponyms of influence include imponderable, imprint, morale builder, canker, pestilence, enticement, temptation.

influence (noun)	support (noun)
causing something without any direct or apparent effort	aiding the cause or policy or interests of
a power to affect persons or events especially power based on prestige etc	the act of bearing the weight of or strengthening
a cognitive factor that tends to have an effect on what you do	documentary validation
one having power to influence another	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 effect of one thing (or person) on another	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

influence (verb)	support (verb)
shape or influence; give direction to	establish or strengthen as with new evidence or facts
induce into action by using one's charm	put up with something or somebody unpleasant
have and exert influence or effect	adopt as a belief
	argue or speak in defense of
	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