Criteria to examine when selecting a book publisher are:
A commercial publisher is an entity for which the core business is producing books and distributing them for sale. Commercial publishers take on a financial risk when committing to publish a book. To minimise risk, they have a selection process. Once a manuscript is selected for publication, the publisher provides copy-editing and proof-reading editorial support. Once published, the publisher provides further investment by marketing the book.
Self publishing, vanity presses and companies that specialise in the publication of theses do not have a selection process, provide little or no editorial support or marketing and so do not meet the definition of a commercial publisher.