As a rule, publishers and agents want only previously unpublished work; I get that.
But, like everyone else, I'm a special snowflake!
I have a collection of children's stories that is being provided to a small (~30) group of friends. This edition will not be publicly available. It will not be advertised.
Does this disqualify the book in most agents' and/or publishers' eyes? If not, would I mention the private edition, and if so, at what point in the process?
A Special Snowflake Thriving in the Texas October Heat
Will it have an ISBN?
That's the kicker.
If it has an ISBN, it's published.
If it does not, it's not (for our purposes here anyway.)
Where you need to be careful is not with publishers and agents who can do anything they want (including taking on books that have already been published) but with contests and awards. Those entry requirements may specify what "published" is, and it may not be as loose a definition as I have here.
You don't want to find out the hard way about this.
I will never forget the sinking feeling in the pit of my sharkly stomach when a book I loved and publicized as hard as I could was not eligible for the Oregon Book Award because the author had done a small print run the previous year. I had to drown my sorrows for a week.