They aren't the same thing at all.

Nor is Mary Sue a purely fanfic phenomenon.  We find her in any kind of writing, including original fiction.  There, she's more commonly known as Self-Insertion -- and ranks right up there with expository lumps, said-bookisms, and inconsistent points of view among the Cardinal Sins of Writing.  All are hallmarks of a beginning author.  (There's no sin in being a beginning author.  Everyone was, at some point.  But ideally one does outgrow the mistakes.)

A Mary Sue is not, really, about putting one's self into a story, despite the term 'self-insertion.'  A Mary Sue (or Larry Stu, for her male counterpart) is about putting an idealized self into a story.  That is a very different thing.

Among the better-known truisms of writing is "Write what you know."  That doesn't mean write yourself, necessarily, but it does entail the merciless plundering of your own experiences, fears, weakenesses, and secret hopes for the small details that flesh out a character and make fiction live.  The difference between a Mary Sue and a semi-autobiographical character (sometimes called an "avatar") is HOW DAMN HONEST you're willing to be.  To write well, the author must be willing to reveal her/himself.  It's akin to standing emotionally naked in front of strangers.  (Hmm, writing as nude dancing ... there's a thought.)  A certain level of raw honesty is what creates the intimate hermaneutic between author and reader that is necessary to draw in a reader and makes him or her care about the characters, and what happens to them.

Can you stand up and tell people about your terrors?  Your most embarrassing moments?  Your private demons and angels?  Your buried shame?  Your sex life?  This isn't about fantasy.  It's about reality.  That's the whole point.  One can't create a GOOD original character, if it's fantasy.

Mary Sue is a fantasy.

She may not always be Polly Anna Perfect, but she's imperfect in "charming" ways.  The perky, pretty, hot-tempered heroine (or hero) who gets the guy/gal and/or saves the day.  Real people are more complex than that.  They make mistakes, they do stupid and cruel things -- intentionally or not so.  Their unattractive sides are unattractive.  An original character in fanfic may still save the day, but real characters interact with the other characters.  They're part of the web of the tale, even if they're the protagonist.  Original characters -- like any good character -- should be shaded and complex, and have room to grow as human beings.  Readers are far more interested in how people surmount the various challenges of life.

Why one writes (and reads) fanfic sometimes has a big influence on the presence, or absence, of Mary Sues in writing.  Fanfic is a special category; people are playing in others' sandboxes, and they're not trying to sell the results.  Writing workshops attempt to kill self-insertion (among other things).  But in fanfic?  <shrug>  I'd argue it has a place.  I don't read such stories because I don't read stories for that reason.  Nor would I say they're "good" stories, by the criteria of formal writing.  But some people read and write fanfic as an escape.  They WANT the fantasy.  That's why PWP smut romps are popular, too.  Fantasy.  Hot bodies doing interesting (and sometimes biologically improbable) things.

But myself, I write fiction as a road to reality.  Art reflects life.  I write about the real world -- even if it's one that includes mutants and wizards and aliens.  I write to get it out of my head; I bleed on the page because it's how I stay sane.  Writing as therapy?  Maybe. :)   But one must still learn to make it marketable.  Purely theraputic writing is no more readable than the escapist Mary Sue.

And that's the real difference between an original character (in any form of writing) and a Mary Sue.  Original characters are fictional human beings.  Mary Sues are fictional fantasy.  Don't confuse them, and don't assume an original character in fanfic is the author any more than you would assume that of a protagonist in published original fiction.  Occasionally they are.  Far more often, they're not -- even if they share with the author the same gender, race, socio-economic background, or other apparent similarity.  Again, a good author "writes what she knows."  And I would be a very poor writer indeed if all I could write was myself.
 

The Mary Sue Litmus Test -- For a good giggle