daydream vs conceive of

daydream is a noun but conceive of is not a noun.

Word	Noun	Adjective	Verb	Adverb
daydream	Yes	No	Yes	No
conceive of	No	No	Yes	No

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

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

Other hypernyms of daydream include envisage, ideate, imagine.

daydream (noun)	conceive of (noun)
absentminded dreaming while awake

daydream (verb)	conceive of (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