The difference between Dream and Heaven
When used as nouns, dream means imaginary events seen in the mind while sleeping, whereas heaven means the distant sky in which the sun, moon, and stars appear or move.
When used as verbs, dream means to see imaginary events in one's mind while sleeping, whereas heaven means to transport to the abode of god, the gods, or the blessed.
Dream is also adjective with the meaning: ideal.
check bellow for the other definitions of Dream and Heaven
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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
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Heaven as a noun (dated, now usually plural):
The sky, specifically: The distant sky in which the sun, moon, and stars appear or move; the firmament; the celestial spheres. The near sky in which weather, flying animals, etc. appear; the atmosphere; the climate. A model displaying the movement of the celestial bodies, an orrery.
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Heaven as a noun (religion):
The abode of God or the gods, traditionally conceived as beyond the sky; especially: The abode of God and of the angels and saints in His presence. The abode of the Abrahamic God; similar abodes of the gods in other religions and traditions, such as Mount Olympus. Providence, the will of God or the council of the gods; fate.
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Heaven as a noun (religion):
The afterlife of the blessed dead, traditionally conceived as opposed to an afterlife of the wicked and unjust (compare ); specifically: The afterlife of the souls who are not sent to a place of punishment or purification such as hell, purgatory, or limbo; the state or condition of being in the presence of God after death. The afterlife of the blessed dead in other religions and traditions, such as the Pure Land or Elysium. Any paradise; any blissful place or experience. A state of bliss; a peaceful ecstasy. Similarly blissful afterlives, places, or states for particular people, animals, or objects.
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Heaven as a verb (obsolete):
To transport to the abode of God, the gods, or the blessed.
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Heaven as a verb (obsolete):
To beatify, enchant, or please greatly.
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Heaven as a verb (obsolete):
To beautify, to make into a paradise.