cotton on vs comprehend

cotton on and comprehend both are verbs.

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

As verbs, comprehend is a hypernym of cotton on; that is, comprehend is a word with a broader meaning than cotton on:

Other hypernyms of cotton on include apprehend, compass, dig, get the picture, grasp, grok, savvy.

cotton on (verb)	comprehend (verb)
understand, usually after some initial difficulty	get the meaning of something
	to become aware of through the senses
	include in scope; include as part of something broader; have as one's sphere or territory