twig vs catch on

twig is a noun but catch on is not a noun.

Word	Noun	Adjective	Verb	Adverb
twig	Yes	No	Yes	No
catch on	No	No	Yes	No

As verbs, twig and catch on are synonyms defined as:

Other synonyms of twig include cotton on, get it, get onto, get wise, latch on, tumble.

twig (noun)	catch on (noun)
a small branch or division of a branch (especially a terminal division); usually applied to branches of the current or preceding year

twig (verb)	catch on (verb)
branch out in a twiglike manner	become popular
understand, usually after some initial difficulty	understand, usually after some initial difficulty