grok vs cotton on

grok and cotton on both are verbs.

Word	Noun	Adjective	Verb	Adverb
grok	No	No	Yes	No
cotton on	No	No	Yes	No

As verbs, cotton on is a hyponym of grok; that is, cotton on is a word with a more specific, narrower meaning than grok:

Other hyponyms of grok include figure, catch on, get it, get onto, get wise, latch on, tumble, twig, intuit, digest.

grok (verb)	cotton on (verb)
get the meaning of something	understand, usually after some initial difficulty