I've never done the research on how one company is different from the other, but I do know there are lots of print-on-demand services that will be happy to take your money. Basically, unlike a traditional publishing arrangement in which the publisher pays you to print your work, in this case you will be paying the publisher. When they reach a certain threshold in orders, they will print enough copies to fulfill those orders. But you will be on Amazon, and you can set up a Facebook page or whatever to try and build an audience. (Facebook will want some of your money too for sponsored ads an whatnot, otherwise you'll never expand far beyond your friends list.)
True self-publishing means putting up all of your own money to apply for an ISBN, forming your own small business, purchasing your own graphic design software for page layouts (or hiring a talented friend to do that for you), finding a printer willing to accept your small order (several to choose from in the Midwest), and then finding a distributor to help you get your books in stores (don't even think of approaching Barnes & Noble directly). Note that no one will even touch your product if it doesn't have a barcode on the cover, but those can be obtained fairly easily (for about $25-$30, assuming you have an ISBN). The plus side is that any revenue you generate is yours to keep. The downside is that all of the responsibility falls on you. I can attest that this does work in certain niche markets, but I'm not sure that it work as well for fiction.
For a more earnest path to publication, you need to start small and build a resume. Seek out and accept whatever freelance assignments you can get; some of these pay nothing at all, others pay well enough that you'll wish there was more to go around. Just like any endeavor, you need to build a reputation. Everything you publish is a "win" that you can put on your resume. Over time, some publishers will seek you out, rather than vice versa.
If you've written something that you think is truly special, you could always go fishing for a literary agent. Note that most traditional publishers will never accept an unsolicited manuscript, and will happily give you an attitude if you try and contact them directly.
Since this is a CYOA-inspired website, I should point out the history of the actual Choose Your Own Adventure series. That was the brainchild of Edward Packard, who came up with the idea circa 1969. His attempts to publish his first book, Sugarcane Island, were completely unsuccessful. The Vermont publisher R. A. Montgomery was mildly successful publishing the early books on a small scale in the 1970s, but it was basically a lucky break in the early 80s that made the books a commercial success on an international scale
Myself, I have published non-fiction several times since 2001, both through my own small business and through established publishers (one on each coast, now that I think of it). But I am here on this website because a recent attempt to branch into other opportunities hit an abrupt brick wall. Therefore even in the publishing business, past successes is no guarantee of future performance. You are basically trying to rise above a crowd of talented hobbyists and vanity authors, therefore to get noticed you have to demonstrate a talent and an idea that no one else possesses.
And a lucky break here and there doesn't hurt, either.
