dream vs daydream

dream and daydream both are nouns.

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

As nouns, daydream is a hyponym of dream; that is, daydream is a word with a more specific, narrower meaning than dream:

As verbs, dream and daydream are synonyms defined as:

Other synonyms of dream include stargaze, woolgather.

dream (noun)	daydream (noun)
a series of mental images and emotions occurring during sleep	absentminded dreaming while awake
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

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