Let's take a quick moment to review the basic differences between trade publishing, self-publishing, and vanity publishing.
In trade publishing (which is what the majority of the books on your shelves probably went through), you write a book, and the publisher pays you money for it. You retain copyright, and license some number of sub-rights to the publisher. They then pay other people for printing, cover art, copy-editing, etc, and when it's done they recoup those costs (hopefully) by selling the result to bookstores, who sell them to readers. You may be asked to contribute to marketing, or choose to do it on your own. The overall financial risk is shouldered by the publishing company, and they split the profits with you, the writer.
In self-publishing, you act as your own publisher. You contract with people for the above-mentioned services. You retain copyright and (aside from whatever is necessary to get the books printed) retain sub-rights. Once you have books, you a) give them to family and friends (if this was done as a purely personal venture -- like, say, a genealogy) or b) start working your tail off to market the books to a larger readership. Bookstores will probably not buy them from you unless it's local history or some other niche market they have a strong reason to believe will pick your work up, but if you're really good at marketing you may still move enough copies to recoup your costs. The financial risk is shouldered by you, and you keep your profits.
In vanity publishing, you pay a company to act as your publisher. They provide variable services, depending on what you've paid for, usually at low quality and a fairly high markup (since they are now acting as a middle-man between you and the cover artist, etc). You have less control over the result than in self-publishing, and depending on the contract may have signed over a portion of your rights to the company. They may also require you, in that contract, to buy a certain minimum number of your own books. Bookstores will again probably not buy them from you. The company may sell you marketing assistance (again at a markup), or you can take on this burden yourself again. The financial risk is shouldered by you, and the company keeps some percentage of your profits. A vanity press makes its money off writers, not readers.
Harlequin Horizons is a vanity press, not a self-publishing company. It is the monetization of Harlequin's slush pile. Removing the name "Harlequin" from the company is insufficient; they need to stop advertising their vanity press in rejection letters, and implying that paying them to publish your book may result in you being later picked up by a proper Harlequin editor. They are trying to take advantage of aspiring authors, and their spokespeople have consistently and disturbingly worked to blur the clear facts of this case with half-truths and statements that are either outright lies, or demonstrations of resounding ignorance as to how the industry works. RWA has rightly condemned this, and MWA and SFWA have their back. Trust the professional writers' organizations on this. Harlequin has not launched some brave new venture in twenty-first century publishing; they have launched a scam, and it should be condemned as such.
If you want to see the story you wrote printed up as a book, and aren't looking to make a career out of this, go to Lulu. They're honest. Harlequin isn't.