box vs ballot box

box and ballot box both are nouns.

Word	Noun	Adjective	Verb	Adverb
box	Yes	No	Yes	No
ballot box	Yes	No	No	No

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

box (noun)	ballot box (noun)
a blow with the hand (usually on the ear)	a box where voters deposit their ballots
a (usually rectangular) container; may have a lid
separate partitioned area in a public place for a few people
private area in a theater or grandstand where a small group can watch the performance
the driver's seat on a coach
any one of several designated areas on a ball field where the batter or catcher or coaches are positioned
evergreen shrubs or small trees
the quantity contained in a box
a rectangular drawing
a predicament from which a skillful or graceful escape is impossible