dig vs cotton on

dig is a noun but cotton on is not a noun.

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

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

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

dig (noun)	cotton on (noun)
the act of digging
the act of touching someone suddenly with your finger or elbow
a small gouge (as in the cover of a book)
an aggressive remark directed at a person like a missile and intended to have a telling effect
the site of an archeological exploration

dig (verb)	cotton on (verb)
get the meaning of something	understand, usually after some initial difficulty
turn up, loosen, or remove earth
create by digging
remove the inner part or the core of
poke or thrust abruptly
thrust down or into
remove, harvest, or recover by digging
work hard