promote vs campaign

promote is not a noun while campaign is a noun.

Word	Noun	Adjective	Verb	Adverb
promote	No	No	Yes	No
campaign	Yes	No	Yes	No

As verbs, campaign is a hyponym of promote; that is, campaign is a word with a more specific, narrower meaning than promote:

promote: make publicity for; try to sell (a product)
campaign: exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for

Other hyponyms of promote include propagandise, propagandize, plug, bill, agitate, crusade, fight, press, push.

promote (noun)	campaign (noun)
	several related operations aimed at achieving a particular goal (usually within geographical and temporal constraints)
	an overland journey by hunters (especially in Africa)
	a series of actions advancing a principle or tending toward a particular end
	a race between candidates for elective office

promote (verb)	campaign (verb)
make publicity for; try to sell (a product)	go on a campaign; go off to war
change a pawn for a better piece by advancing it to the eighth row, or change a checker piece for a more valuable piece by moving it to the row closest to your opponent	run, stand, or compete for an office or a position
be changed for a superior chess or checker piece	exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for
give a promotion to or assign to a higher position
contribute to the progress or growth of