In my tests it only recognizes the same browser. I’m a different person when using different browsers. I noticed that I can still be correctly fingerprinted after resetting the browser or using a private window.
Using Firefox (on a Linux laptop) with resistfingerpriting=true or Mull (on an Android) with its default settings, I'm able to get assigned a new fingerprint whenever I clear cookies or use a new Incognito session.
I haven't tested it, but presumably they also wouldn't be able to track me between domains, even without clearing cookies.
Doesn’t seem to be the case on iOS unfortunately which is really creepy. Still get tracked regardless of Cookie & Cache Reset/VPN/Private Browsing with Safari