Let's start out with a quick run down on three of the roads to publishing your work: Big Publishing Houses, Vanity Presses, and Independent Publishers.
Hachette Book Group: Authors such as: James Patterson and Nicholas Sparks
HarperCollins: Authors such as Diane Mott Davidson and Edward Abbey
Macmillan: Nonfiction and Genre Fiction, College/Academic, and Journals
Penguin Group: Adult and Children's Fiction, Nonfiction, recent publications by Harlan Cobin and the memoir, Girl Walks in a Bar by SNL Alum Rachel Dratch.
Random House: The Girl With the Dragon Tattoo, Rachel Maddow's Drift.
Simon and Schuster: Authors such as Jodi Picault and Mary Higgins Clark.
Each of these Publishing Houses has their own "Imprints" which fall under the umbrella of the larger company name. Each Imprint carries its own genre. So, for example, Hachette Book Group owns Little, Brown, & Company and Grand Central Publishing. Little, Brown, & Company carries the Imprint Back Bay Books, which publishes literary fiction, including contemporary writers like David Sedaris and new editions of classics like C.S. Forester's Hornblower series.
These publishing houses do not accept unsolicited manuscripts. With few exceptions, the only way to publish your work through these houses is with an agent. It's an excellent goal to want your novel or nonfiction published by these organizations, but your best bet is to find a great agent to get you there.
At the other end of the spectrum are what are called "Vanity Presses." This is not the same as an Independent Press. A Vanity Press is one you pay to publish your work. They often provide cover art and may do editing for a fee, but they are basically a means to publication you pay for yourself. The plus to these is you have a book at the end of the deal. The negative is, unless you hire an outside book coach or line editor, the likelihood for grammatical and typographical errors is very high.
Agents, editors, and publishers work with an author to get material ready for publication. If you go the Vanity route, you probably have only yourself and maybe a friend as a proofreader. With no outside eye, your work may not be as polished as it would be through an agent and a professional publishing house. This includes conceptual aspects such as story structure, voice, and plot. A good team working with you may help you improve your book, not just find the missing commas and to, too, twos.
Why, then, might you publish in this way? Perhaps you've written a book on your family history, your community, or a specific event, and you'd like to give them as gifts or sell locally. Especially if you have used the services of an editor, this is a viable way to go. A Vanity Press doesn't mean the author is bad, though it is often viewed that way. It's also unlikely to provide you access to agents or a big name publisher unless you sell several thousand books on your own.
E-Books or Electronic Books are books made available for reading on electronic devices such as a Kindle, Nook, or computer. These may be books originally published in hard or paperback versions, though some books go directly to E-Book or E-publishing and aren't available through standard hard or soft cover publishing. E-Book refers to the fact it is a digital book, not a specific publisher, nor whether a book is agented and vetted or self-published.
On-Demand: (POD) Like E-Books, this term describes the process, not the publishing. A book available "On-Demand" is only printed when ordered. Again, this may be a self-published book, where the author pays a fee and sets up their books to be published when ordered. POD is also used, for example, by University Presses, saving the organization from having to print huge numbers of books that must be stored. By printing only books sold, there are no leftover books. There is a move in the publishing industry to shift into more of this type of technology, saving the publishing houses from vast pallets of unsold books. There is also a move on the retail end to provide machines (think Xerox on steroids) where a buyer can pay for a book, type in the title, and 15 minutes later a bound, paper copy comes sliding out. Think of the shelf space this would save! It also can provide access to books no longer in print. But keep in mind, like E-Books, someone has to have input all the words of that manuscript into the system before it's available. It's not a fast easy process.
These are smaller, typically genre specific, publishing houses that work with both agented and unagented authors. Unlike self-publishing, authors don't pay a fee to be published, but, like the large publishing houses, authors must be accepted by the publisher. Most Independent Publishers have editors on staff, and material is vetted, improved, and line edited prior to publication. These publishers often have artists or art departments to work on cover art and can assist with author PR and sales. Authors receive a percentage of sales from the books. Because of the smaller size, they carry less authors, however, they may be able to give their authors more personal attention.
These publishers are also often willing to look at unpublished authors and submissions can be made without an agent. This is a great way for new writers to get the assistance of an editor and publishing team, without the stigma of self-publishing. But again, your work must be accepted by the publisher, so don't submit until your manuscript is perfect! And, do your homework, find the Independent Press that publishes your genre. They can be just as discriminating as a large press and, while they are likely to take on new writers, the quality has to be high because they don't have the "big name" writers selling millions of copies to cover the losses of a less popular book.