What's the difference between 成人 and 大人 ?
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成人 is a very specific term and refers to persons who reached the age of 20 and above. It's derived from the definition of the Japanese law, which says "年齢二十歳をもって、成年とする".
You used to get drafted and taxed after this age. In today's context, it's the legal drinking/smoking age.
大人 is a more lax term and usually means persons that are older than around 18 - 25 (depends on the context/speaker).
大人 is also used to mean "mature". For example, a toddler can be 大人 like this:
You can't do this with 成人. It's also more formal than 大人 so it's much more common to use 大人 in everyday speech. Also 成人になる specifically means "to turn 20". 大人になる usually means "to become mature".
This is what I found in my dictionary. Considering I'm not actually an expert, or even an intermediate at reading Japanese, it might not be the definite answer you're looking for.
But since it was impossible to post it as a comment, I'm writing it as an answer:
The thesaurus is "Tsukaikata no Wakaru Ruigo Reikai Jiten" (使い方の分かる類語例解辞典), which is provided by the Japanese publisher Shogakukan.
成人 means adult or to mature or to grow up. 大人 just means adult.
You may use 大人 as "Only adults can see this film" I'd treat it like a noun. 大人だけこの映画が見える。
For 成人 you may use it in a similar context as above or you can say someone has grown up. In the next example. Sandra has grown up to be a beautiful woman.