And there are even other sorts of things, many many other sorts.
"Would you be willing to run this world I find interesting? I'm happy to help you with <X problems the player knows their GM friend has> in return." (If you wish to view it as such, "payment for services rendered".)
"Would you be willing to run this world I find interesting, since I ran that campaign you wanted last year?" (Tit-for-tat in the other direction, "I already did a thing for you".)
"I know you mentioned you've been feeling a little burned out with D&D, especially with the recent rule changes. I recently bought Energized with a Cataclysm, it's a pretty simple system, would you be willing to run that?" (Proposing as a palate-cleanser.)
"I know you're skeptical about Orientalist tropes, but I've been hankering for some cool samurai action. Would you consider running Ryu & Ronin? It was made with loving attention to authentic Japanese history!" (Recognizing limitations, and specifically looking to address them, not override them.)
You can come up with a nigh-infinite variety of terms, all of which actually do respect the personal interests and preferences of the other person. None of them involve absolute power. None of them involve one person laying down the law from on high.