sprain vs wrench

sprain and wrench both are nouns.

Word	Noun	Adjective	Verb	Adverb
sprain	Yes	No	Yes	No
wrench	Yes	No	Yes	No

As nouns, wrench is a hypernym of sprain; that is, wrench is a word with a broader meaning than sprain:

sprain: a painful injury to a joint caused by a sudden wrenching of its ligaments
wrench: a sharp strain on muscles or ligaments

Other hypernyms of sprain include pull, twist.

As verbs, sprain and wrench are synonyms defined as:

Other synonyms of sprain include rick, turn, twist, wrick.

sprain (noun)	wrench (noun)
a painful injury to a joint caused by a sudden wrenching of its ligaments	a hand tool that is used to hold or twist a nut or bolt
	a jerky pulling movement
	a sharp strain on muscles or ligaments

sprain (verb)	wrench (verb)
twist suddenly so as to sprain	twist suddenly so as to sprain
	twist or pull violently or suddenly, especially so as to remove (something) from that to which it is attached or from where it originates
	twist and compress, as if in pain or anguish
	make a sudden twisting motion