Publishing runs on selling books. If a publisher doesn't think a book will sell, they won't publish it. However, vanity presses run on selling services to authors. They'll publish anything if they're paid to. But they won't sell any copies, and bookshops won't stock what they print.
Vanity presses are still publishers. I can publish my own book and be considered a publisher. So your statement that publishers don't make pay to publish is misleading is all I'm saying.
You are splitting hairs here. There is an important and very pertinent difference between vanity presses and real publishers. The whole distribution step(and getting into libraries). In facts real publishers are not just printers, they are a whole value chain.
an author can pay a vanity press for all of those services. right or wrong, they’re still publishers. they do the same thing a “real publisher” does but you pay them instead them paying you. again right or wrong, vanity presses still publish the book. it still gets printed. it still gets released.
And the point of the post is, that that isn’t really a publisher as such. And should not be categorized with “real” publishers. I am not saying vanity publishers do not have their uses. Being paid for your work as an author, that is a real thing.