stool vs dog shit

stool and dog shit both are nouns.

Word	Noun	Adjective	Verb	Adverb
stool	Yes	No	Yes	No
dog shit	Yes	No	No	No

As nouns, dog shit is a hyponym of stool; that is, dog shit is a word with a more specific, narrower meaning than stool:

Other hyponyms of stool include dog do, dog turd, doggy do, crap, dirt, poop, shit, shite, turd, droppings, dung, muck, meconium, melaena, melena.

stool (noun)	dog shit (noun)
a simple seat without a back or arms	fecal droppings from a dog
a plumbing fixture for defecation and urination
(forestry) the stump of a tree that has been felled or headed for the production of saplings
solid excretory product evacuated from the bowels

stool (verb)	dog shit (verb)
have a bowel movement
grow shoots in the form of stools or tillers
react to a decoy, of wildfowl
lure with a stool, as of wild fowl