footbath vs bathing tub

footbath and bathing tub both are nouns.

Word	Noun	Adjective	Verb	Adverb
footbath	Yes	No	No	No
bathing tub	Yes	No	No	No

As nouns, bathing tub is a hypernym of footbath; that is, bathing tub is a word with a broader meaning than footbath:

footbath: a small bathtub for warming or washing or disinfecting the feet
bathing tub: a relatively large open container that you fill with water and use to wash the body

Other hypernyms of footbath include bathtub, tub.

footbath (noun)	bathing tub (noun)
a small bathtub for warming or washing or disinfecting the feet	a relatively large open container that you fill with water and use to wash the body