daydream vs ideate

daydream is a noun but ideate is not a noun.

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

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

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

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

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

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