Most places only purchase the one-time, nonexclusive right to publish. There is usually an exclusivity period, during which you can’t publish elsewhere but when that period is over you are free to publish on Medium (or anywhere else) Some venues ask that when you do so you indicate that they published it first. A few places — the New York Times, for instance — purchase ALL rights. So once you’ve signed their contract and they publish and pay for your work, they own it. You can’t post it on Medium without paying them for the right to do so. But? They pay well and they will bring millions of readers to you work.