daydream vs dream

daydream and dream both are nouns.

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

As nouns, dream is a hypernym of daydream; that is, dream is a word with a broader meaning than daydream:

Other hypernyms of daydream include dreaming.

As verbs, daydream and dream are synonyms defined as:

Other synonyms of daydream include stargaze, woolgather.

daydream (noun)	dream (noun)
absentminded dreaming while awake	a series of mental images and emotions occurring during sleep
	imaginative thoughts indulged in while awake
	a fantastic but vain hope (from fantasies induced by the opium pipe)
	a state of mind characterized by abstraction and release from reality
	a cherished desire
	someone or something wonderful

daydream (verb)	dream (verb)
have a daydream; indulge in a fantasy	have a daydream; indulge in a fantasy
have dreamlike musings or fantasies while awake	experience while sleeping