They're the same dog.
Rover from Carousel of Progress and the jail dog holding the keys in Pirates of the Caribbean are the same character — confirmed by Cast Members on the Keys to the Kingdom tour.
And it gets better. The unofficial Cast Member backstory from the 1990s says Rover was part of a litter of five pups — Rover, Queenie, Sport, Spot, and Bony. Rover and his siblings appeared in the various Carousel of Progress scenes across the decades, while Bony wound up in the Haunted Mansion as the Caretaker's dog.
One family. Three parks. Completely unbothered by any of it.
The Dog Person tee puts all three together — Rover living his best life with John's family through the 20th century, Bony cowering at the graveyard gate, and whoever drew the short straw and ended up in a jail cell holding the keys for a bunch of pirates who cannot figure out how to ask nicely.
This is for the Disney adults who know this lore. And for the ones who just found out and are now standing still somewhere processing it.
Good dog. Great dog. Arguably the most well-traveled dog in Florida.