Mainz-Kastel is a district of Wiesbaden, right across from Mainz. As the name implies, it used to be a part of Mainz, but after WWII, the Rhine was a convenient border between the French and US occupied regions, so it was made a part of Wiesbaden. Culturally, Mainz-Kastel is very much Mainz though, sharing for example the tradition of "Fassenacht", Mainz Carnival.
So most people there feel like being Mainzer, and enjoy the beautiful view from across the river onto the Mainzer Schloss (Palace).