going under vs sinking

going under and sinking both are nouns.

Word	Noun	Adjective	Verb	Adverb
going under	Yes	No	No	No
sinking	Yes	No	No	No

As nouns, sinking is a hypernym of going under; that is, sinking is a word with a broader meaning than going under:

going under (noun)	sinking (noun)
(of a ship) sinking	a descent as through liquid (especially through water)
	a slow fall or decline (as for lack of strength)
	a feeling caused by uneasiness or apprehension