Generally.

Publishers fund all or part the game, advertise the game, and give logistical support for the game.

In return publishers take a share of the money the game earns.

Depending on the publisher they can make demands on the developers or won't.

Like ea for example generally has a hands off approach..they give the dev team a bag of money and then say make your game but I expect 2 bags of money back idc how your get it.

Other companies especially in the past had rules. Like in older days publishers would force games to be difficult so you couldn't beat the game if you rented it