Part of it just has to do with what you call it, I think. But mainly, it's the size and how open you're making it.
I mean, in my head, a group PSL isn't really run by one person, it's a small group of people playing and plotting out something, but no one's really In Charge. Or maybe you just want to limit it to five or six people or characters. It's for smaller, more in-depth plots than you'd get in a large game, or perhaps just for a universe that's very small.
I don't think there are any rules at all, it's just how you want to run it.