bathing tub vs hot tub

bathing tub and hot tub both are nouns.

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

As nouns, hot tub is a hyponym of bathing tub; that is, hot tub is a word with a more specific, narrower meaning than bathing tub:

bathing tub: a relatively large open container that you fill with water and use to wash the body
hot tub: a very large tub (large enough for more than one bather) filled with hot water

Other hyponyms of bathing tub include footbath, hip bath, sitz bath.

bathing tub (noun)	hot tub (noun)
a relatively large open container that you fill with water and use to wash the body	a very large tub (large enough for more than one bather) filled with hot water