According to my dictionary*, “publish” means “to make public; to proclaim, promulgate; to cause to be printed and offered for sale”. That means that each edition of each and every book can only be published once, when its publisher first makes it available for sale on its publication day.
Books are not published one copy at a time; they are published one edition at a time. Individual copies of each edition are sold as the orders come in, but each time an order is fulfilled that doesn’t mean that the book has been published all over again: it means that someone has bought a copy, that’s all. When an edition sells out further copies might be printed but that’s not a new publication, it’s a reprinting of an existing edition. If a book were to be substantially changed then that would result in a new edition, which would have its own publication date: but it would not be an entirely new publication, just a new edition of a previously published book.
So when you read publishers claiming that POD means “publish on demand”, you will now realise that this is a nonsense. POD refers to the printing technology known as “print on demand” and nothing else.
The use of POD technology isn’t restricted to the smaller or dodgier publishing houses: some of the larger publishers use it to keep older books in print (which has its own, somewhat worrying, implications). But generally, if a publisher uses the phrase “publish on demand” you should be wary of them: they’re in bad company. The phrase was coined originally by PublishAmerica, which is one of the grand masters of vanity publishing and the weasel-wording which is associated with such practices. It’s a meaningless term which is designed to confuse.
Publishers which rely solely on POD technology to print their books are generally either unwilling or unable to invest their own money in printing reasonable runs of the books that they publish: and whatever their reasons for using only POD, they are best avoided. If you don’t believe me, read Lynn Price on the subject: she knows what she’s talking about.
*My dictionary is so old and tatty that it’s lost its cover and several pages, front and back, otherwise I’d attribute it properly here. Apologies to whoever wrote and published it: I owe you a credit.