As I understand it, ISBNs are specific to author/publisher/edition, so if you have a book published in hardcover, the paperback gets a different ISBN, the ebook gets a third ISBN, and if it's picked up by a different publisher, you start over again.
Also, Smashwords is your publisher. They're packaging the book. They're selling it. They are, in other words, publishing it. So yeah, the ISBN would reflect that they're your publisher.
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