twitching vs muscle spasm

twitching and muscle spasm both are nouns.

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

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

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

Other hypernyms of twitching include cramp, spasm.

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