The book industry really only uses one metric to distinguish between publishers and non-publishers. If you own an ISBN block, you're a publisher. The ISBN number is the key value that identifies the publisher of a book in all of the online databases and inventory systems used world-wide. I've heard that in some countries you can obtain an ISBN number for free, but in the U.S., you have to deal with the Bowker agency, where "agency" has a special legal meaning, that they've been granted a monopoly franchise by the government. The last ISBN block I purchased consisted of 10 numbers (enough for ten titles) and cost around $250 with the additional publisher registration charge. They call it an "application process," but I've never heard of anybody failing.
All it takes to obtain an ISBN number is a credit card (or a check and a lot of patience), but it's only the first step in the process. Bowker will aggressively market add-on services to you that I've never seen any need for, they really stretch the use of statistics for sales pitches in strange, new ways. You can generate bar codes for your book covers for free with Bookland, and you can convert older 10-digit ISBN's to 13-digit ISBN's for free as well. Don't get panicked into thinking you need to change your existing book covers, the new system grandfathers in books published with the 10 digit ISBN's.
So, now you know how to obtain an ISBN number, buy it from Bowker, but that's not the end of the story. You'll want to get your ISBN information registered with Books-In-Print, and the only practical way to do that is to sign up for BowkerLink (the only free service they have), the online tool for uploading book information, including price, page count, distribution, etc. It is one of the worst software interfaces I've used in my life, but that's the price of dealing with a monopoly.
Obtaining an ISBN number makes you a publisher in the eyes on the book industry, but it won't sell any books for you, no matter how many add-on services you pay for. The supply exceeds the demand for new titles, most never see the light of a bookstore shelf or sell much beyond the author's family and friends. Using a subsidy press to publish your book doesn't make you a self-publisher unless you own the ISBN number on the cover. One of the common misconceptions about self publishing is that you don't have to obtain your own ISBN number to become a publisher if you pay a subsidy press to publish your book. If it's their ISBN, they are the publisher, not you.
You can publish books on a shoestring and you can even succeed, but you can't pretend it's a publishing business without first obtaining an ISBN number. Spend the $250 now, even if it means skipping a few meals, or you'll regret it for the rest of your publishing life. Bookselling is all about marketing, and establishing yourself as publisher with an ISBN is the easiest (and cheapest) step in the path.