What is the difference between 才 and 歳

私は二十一歳です。
私は二十一才です。
Are both sentence right?

The proper kanji for age is 歳. Originally, 才 only denotes one’s talent and does not carry a meaning of age. But the character 歳 is difficult to write, so the homonym 才 is used instead. Nowadays, 才 is considered a 略字 (りゃくじ) of 歳. With that said, 才 is now used in almost everywhere and 歳 is reserved for the more formal writings.

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@pts I think it might be considered a 代用字 opposed to 略字

@Tobata Both sentences are correct! I would write them this way:
私は21歳です。
私は21才です。

Since you’re 21, IMHO, I think it looks more appropriate using 歳

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