campaign vs senate race

campaign and senate race both are nouns.

Word	Noun	Adjective	Verb	Adverb
campaign	Yes	No	Yes	No
senate race	Yes	No	No	No

As nouns, senate race is a hyponym of campaign; that is, senate race is a word with a more specific, narrower meaning than campaign:

Other hyponyms of campaign include campaign for governor, governor's race, senate campaign.

campaign (noun)	senate race (noun)
several related operations aimed at achieving a particular goal (usually within geographical and temporal constraints)	a race for election to the senate
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

campaign (verb)	senate race (verb)
go on a campaign; go off to war
run, stand, or compete for an office or a position
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