GREAT question! This is where the difference between Masters and Publishing comes into play.
Masters are the actual recording of the song (the .mp3 file), so when a song is streamed or sampled, that file is used and the owner of that part is paid. Masters are the one final condensed file – that ‘master’ file.
Publishing is the concept of the song (the arrangement). Think of this as all the different stems and layers that you see in Logic or a program you are mixing on. So when you cover it, or re-record it, you are creating a new .mp3 but using the same concept … so the person owning the publishing is paid.
It gets a lot more complicated, but that’s for starters.
So Scooter Braun bought and re-sold the Masters of Taylor Swifts catalog, but she still owns the publishing (or concept of the song). So she can re-record those songs and create new ‘master’ files that will be new .mp3s. Now she owns the new rendition because she will own the new masters and she still owns the publishing.