The difference between Daydream and Dream
When used as nouns, daydream means a spontaneous and fanciful series of thoughts while awake not connected to immediate reality, whereas dream means imaginary events seen in the mind while sleeping.
When used as verbs, daydream means to have such a series of thoughts, whereas dream means to see imaginary events in one's mind while sleeping.
Dream is also adjective with the meaning: ideal.
check bellow for the other definitions of Daydream and Dream
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Daydream as a noun:
A spontaneous and fanciful series of thoughts while awake not connected to immediate reality.
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Daydream as a verb:
To have such a series of thoughts; to woolgather.
Examples:
"Stop daydreaming and get back to work!"
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Dream as a noun:
Imaginary events seen in the mind while sleeping.
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Dream as a noun:
A hope or wish.
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Dream as a noun:
A visionary scheme; a wild conceit; an idle fancy.
Examples:
"a dream of bliss;  the dream of his youth"
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Dream as a verb (intransitive):
To see imaginary events in one's mind while sleeping.
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Dream as a verb (intransitive):
To hope, to wish.
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Dream as a verb (intransitive):
To daydream.
Examples:
"Stop dreaming and get back to work."
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Dream as a verb (transitive):
To envision as an imaginary experience (usually when asleep).
Examples:
"I dreamed a vivid dream last night."
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Dream as a verb (intransitive):
To consider the possibility (of).
Examples:
"I wouldn't dream of snubbing you in public."
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Dream as an adjective:
ideal; perfect