Subsidy publishing requires the author to pay a fee to the publisher. In self-publishing, the author is the publisher and does not have to pay anyone else to be published.
With subsidy publishers, authors either purchase their books upfront and then sell their books, hoping to sell enough to make a profit, or they split their royalties with the publisher. With self-publishing, authors assume all of the financial burden and all of the profit.
The ISBN, International Standard Book Number, is registered to the subsidy publisher, or in the case of self-publishing, to the author or the author's own imprint.
Subsidy publishers may dictate the price of the book, based on the number of pages and type of book (hardcover, trade paperback or mass market paperback). Self published authors select and price their own books.
Authors retain their copyright when self-publishing. This is typically true when subsidy publishing too, but authors must investigate thoroughly, as some subsidy publishers do assume limited publishing rights.
Some subsidy publishers will manage inventory by printing books on demand and even sending them out to buyers. Self-published authors may also use print on demand services, but often house and manage their own inventory as well as distribute the books themselves.
Subsidy publishers often provide packages for publishing and marketing services, such as editing, cover art design and promotion. With self-publishing, the author must educate himself in all of these areas and perform, or contract out, these services himself.
Today, many authors are self-publishing through epublishing platforms, like Smashwords, Kindle or Calibre. As with self-publishing physical books, authors retain complete control over their work. With the exception of Calibre, a free self-publishing platform, the author must pay a fee and/or the publisher receives a share of the royalties for distribution of the ebook through their selected epublishing platform
Even in the epublishing world, however, authors can elect to go it alone. They need only convert their manuscript into a format that readers can accept, which may be as simply as a pdf file, and set up a mechanism for distributing their book and accepting payment. This can be done directly from their own website, although working through one of the larger epublishing platforms quickly opens them up to a much wider market.