Peyton Manning felt like the first one. Obviously he wasn’t literally, but he felt like it.
Seeing a quarterback who seemingly “belongs” to one franchise suit up in another uniform never feels quite right. Obviously Manning eventually won a Super Bowl with his second team, the Denver Broncos, (it never felt right seeing DeMarcus Ware there either) and Tom Brady lifted the Lombardi Trophy with the Tampa Bay Buccaneers. They may be the exceptions, but looking around the NFL it isn’t hard to find other longtime quarterbacks in similar boats.
Aaron Rodgers obviously plays for the New York Jets.