This should be a simple answer but with today's new technology in self-printing/publication services provided such as from MagCloud, this question becomes much more more complicated. It's very similar to the world of photographers where more and more quality DSLR cameras are more affordable and its easier to become a "pro photographer", its the same in this situation with magazines.
A magazine publication is a company that produces a paperback or/and online publication with articles and spreads, both having advertisers. Having the advertisers is what actually makes a magazine publication credible. No credibility, you're not considered a magazine publication at all. You could have 1 billion free or paid subscribers, no advertisers, you're nothing.
Why I'm pointing this out you may ask?
Because a lot of times I see on my facebook feed about models and photographers being "published" into these so called magazines where the magazine does not pay anyone, may not have any paid subscribers, and defiantly does not have paying advertisers. No credibility. And these folks are cheering on for being published into a no name publication.