fox-trot vs ballroom dancing

fox-trot and ballroom dancing both are nouns.

Word	Noun	Adjective	Verb	Adverb
fox-trot	Yes	No	No	No
ballroom dancing	Yes	No	No	No

As nouns, ballroom dancing is a hypernym of fox-trot; that is, ballroom dancing is a word with a broader meaning than fox-trot:

fox-trot: a ballroom dance in quadruple time; combines short and long and fast and slow steps fixed sequences
ballroom dancing: any of a variety of social dances performed by couples in a ballroom

Other hypernyms of fox-trot include ballroom dance.

fox-trot (noun)	ballroom dancing (noun)
a ballroom dance in quadruple time; combines short and long and fast and slow steps fixed sequences	any of a variety of social dances performed by couples in a ballroom