Real Self-Publishing
The ISBN (International Standard Book Number) ties a book to its publisher. 

If You Are Not The Publisher, You Are Not A Self- Publisher, Nor Are You Self-Publishing. The Publisher owns the ISBN used to identify your book. If you do not own the ISBN that appears in and on your book, you are not the publisher, nor are you self-publishing.

If you are not the publisher but are paying a publisher to publish your book, your book is being published by a vanity publisher. Period. No matter what they call themselves.
(from Publishing Basics)

 

A real self-publisher is an author who has established a small company that tries to make money by selling books to readers.
 
Vanity publishers make most of their money by selling services to naive writers, not by selling books to readers. The books are often ugly, error-filled and overpriced -- and very few copies are sold.
 
Just as no one can eat lunch for you, no other person or company can self-publish for you. The words just don't make sense.
 
OTOH, a "real" self-publisher establishes a business, hires editors and designers, purchases photography, owns ISBNS, obtains LCCNs and copyrights, chooses a printer, and promotes the books.
 
That's very different from buying a "publishing package" from a vanity publisher.