Simile
A simile is a comparison between two unlike things using "like" or "as" to show their similarity.
Her smile was as bright as the sun.
He is as brave as a lion.
(It highlights a shared quality between two different things, but keeps them as separate entities.)
Metaphor
A metaphor makes a direct comparison by stating one thing is another, without using "like" or "as".
Her smile was sunshine.
He is a lion in battle.
(It implies that the subject possesses the qualities of the other thing being compared, making the comparison more forceful and direct.)
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