Of course most sites that try to track you are also storing cookies or local storage. It only takes one to tie your two unique fingerprints together... of course your IP address might suffice. Or account/email address, if you're logged into a site that shares data with third parties and use the same address.

I'm sure someone's also devised a way to guess how to bind two fingerprints together when OS or browser updates but many other parameters (timezone, ip, language, screen size, fonts, etc) remain similar enough.