dream vs daydreaming

dream and daydreaming both are nouns.

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

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

dream (noun)	daydreaming (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)	daydreaming (verb)
have a daydream; indulge in a fantasy
experience while sleeping