daydream vs imagine

daydream is a noun but imagine is not a noun.

Word	Noun	Adjective	Verb	Adverb
daydream	Yes	No	Yes	No
imagine	No	No	Yes	No

As verbs, imagine is a hypernym of daydream; that is, imagine is a word with a broader meaning than daydream:

daydream: have a daydream; indulge in a fantasy
imagine: form a mental image of something that is not present or that is not the case

Other hypernyms of daydream include conceive of, envisage, ideate.

daydream (noun)	imagine (noun)
absentminded dreaming while awake

daydream (verb)	imagine (verb)
have a daydream; indulge in a fantasy	expect, believe, or suppose
have dreamlike musings or fantasies while awake	form a mental image of something that is not present or that is not the case