My search for one thing brought me to a clear and concise answer to a question that doesn’t always have a straight answer. Or at least the answer is still defining itself in the ever-changing publishing world.
Victoria Bindery—a book binding company in British Columbia—defines self-publishing on the FAQ page #14:
What is self-publishing? Self-publishing is the publication of any book or other media by the author of the work, without the involvement of an established third-party publisher. The author is responsible and in control of entire process including design (cover/interior), formats, price, distribution, marketing & PR.
That is exactly the way I defined self-publishing in my post Four Types of Publishing except I used more words.