Steam Direct is the current way to publish games on Steam. In the old days Steam was very picky about who could publish games. This changed many years ago with Steam Greenlight. In this system devs would pay a 1 time fee of 100 USD to submit as many games as they wanted. Then the community would vote on weather they would buy the game or not. Steam would then publish games that had enough votes. (Note Steam Greelight money went to charity.)
Fast forward to June 13, 2017 (The day Steam launched Steam Direct.) This requires a payment of 100 USD for every title, but you can recoup your money if you make 1000 USD in net sales.