Did I get scammed on the taxi fare to Songdo?

I took a taxi from Seoul to Songdo, Incheon, but the driver started without turning on the meter, so I requested him to do so. However, he immediately applied the out-of-town fare within Seoul. When I asked in the middle of the ride, he said not to worry because the GPS would take care of everything, and I noticed there was a 20% additional charge on the meter. When I asked AI, it confirmed that the driver's statement was correct. At the end, when I paid through Uber, the meter showed 41,000 won, but the charge was 36,000 won. When I asked why the amounts were different, he just kept repeating that it was 36,000 won. I also took a picture of the driver's license, so it seemed like I was considering reporting him. I'm curious if this situation was an attempt at fraud. I heard that taking a Kakao taxi from Mokdong to Songdo would cost about 35,000 won.