What are the choices in publishing models?
There are currently three strong models for publishing in North America.
Traditional publishing is where a house/company vets and approves your book, creates the product and pays you small royalties based on sales. In addition to the work of the publisher, you will still need to take an active role in marketing the book.
Hybrid publishing uses the same vetting and acquisition process, and you as an author may help offset the cost of the publishing of the book by helping pay for the production of the book (a fee) ahead of time or, in some cases, by offsetting the cost against future royalties. Royalties in this model are usually and significantly higher as you have already helped pay for the production of the book. Both the publisher and the author share the load on marketing the book.
In Self Publishing, you are fully and completely responsible for your work. You and you alone determine it the book is even worth publishing. You might hire freelancers here and there to help, but the risk and reward(?) are all yours. All marketing is up to you.
Note well that vanity-style publishers will publish absolutely any trash you bring them as long as you have the money. The traditional and hybrid models are not the same as vanity publishing. This is an important distinction.