droop vs slouch

droop and slouch both are nouns.

Word	Noun	Adjective	Verb	Adverb
droop	Yes	No	Yes	No
slouch	Yes	No	Yes	No

As verbs, slouch is a hyponym of droop; that is, slouch is a word with a more specific, narrower meaning than droop:

droop: droop, sink, or settle from or as if from pressure or loss of tautness
slouch: assume a drooping posture or carriage

Other hyponyms of droop include slump, bag.

droop (noun)	slouch (noun)
a shape that sags	a stooping carriage in standing and walking
	an incompetent person; usually used in negative constructions

droop (verb)	slouch (verb)
become limp	walk slovenly
droop, sink, or settle from or as if from pressure or loss of tautness	assume a drooping posture or carriage
hang loosely or laxly