How is a self-insertion different from a mary sue?

Self-insertions aren't always Mary-Sues. Self-insertions tend to become Mary-Sues, but aren't always.

From what I know, Mary-Sues are the "Perfect" characters; beautiful, smart, incredibly strong, no weaknesses whatsoever. A classic trait Mary-Sues always seem to have is mastering every fighting ability available in whatever universe they're inserted in. Read the fic "the Many Loves of Mari Su" bởi xenu1275; it's a good example. It's not of a self-insertion, though, but...

....Sorry, I rambled too much... =.= Hope it helped, though!

It's not.

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My guess is that self-insertion is intentionally using the tác giả as a character/narrator in the story, whereas a Mary-Sue is an tác giả creating what is supposed to be an original character, but is intact, mostly themselves.

A self-insertion is where the tác giả writes himself/herself into the story hoặc bases a character strongly on himself/herself.

A Mary Sue is an overly perfect character. They're usually described in flowery OTT paragraphs, are brilliant at everything, everyone in the story loves them, they become the tình yêu interest of the hero whom the tác giả likes, they might befriend hoặc be related to another favourite character, they're stronger/more powerful/more magical than any other character in the story, they save the day.... Mary Sues generally irritate readers and are boring to read about.

Sometimes self-inserts can become Mary Sues because the tác giả can struggle to criticise himself/herself enough. Other times, if the author's careful to avoid this, the self-insert can work. Mary Sues can also be non-self-based but still too much of a vision of perfection. Self-inserts and Mary Sues can also work if they're done tongue in cheek.