twitching vs spasm

twitching and spasm both are nouns.

Word	Noun	Adjective	Verb	Adverb
twitching	Yes	No	No	No
spasm	Yes	No	No	No

As nouns, spasm is a hypernym of twitching; that is, spasm is a word with a broader meaning than twitching:

twitching: a sudden muscle spasm; especially one caused by a nervous condition
spasm: a painful and involuntary muscular contraction

Other hypernyms of twitching include cramp, muscle spasm.

twitching (noun)	spasm (noun)
a sudden muscle spasm; especially one caused by a nervous condition	(pathology) sudden constriction of a hollow organ (as a blood vessel)
	a painful and involuntary muscular contraction