Curated vs Published : What's the Difference?

There are a lot of writing competitions on the web; a lot of chances to have your work read and published.

I will note a difference between "curated" and "published". This website is starts out as a bunch of notepad files, joined and hyperlinked together, with a script of my own devising adding all the menus, footers, backgrounds and so on... did I mention I'm an IT guy by day?
So I can publish whatever I want - this is my website. Does it make it any good? I'll let you be the judge of that, but typically, no.

A site that was accepting entries into a competition drew this distinction; she didn't want "curated" stories entering her competition. She felt that by having a professional editor putting their considered effort into a story, it would disadvantage other entrants.
Fair enough? It should be, for just about every other competition disallows previously-published stories.
But published? On a site like this one? What about shared as a document online for feedback from a critique group?
Why should that disqualify a story from potentially winning a competition and / or reaching a wider audience?

There's a case of "Initial Publishing Rights", where I understand exclusivity is important. The barrier to self-publishing is SO low, even if you haven't written a handy-dandy script to knit your pages together. Quality has always been worth striving for.

Understand what the competition wants and what they can and will do with your story afterwards. What the scrupulous ones WON'T do, is steal your ideas. Those are safe. Keep working on them.