Sandshoe

According to the Eleventh and War Doctors, the Tenth Doctor wore sandshoes. (TV: The Day of the Doctor) He himself generally called them trainers. (TV: Time Crash)

Behind the scenes
Sandshoe is a primarily Scottish or Australasian word for a sneaker. The implication in the scene is that the Tenth Doctor thought they were shoes meant for serious activity, whereas his other selves thought they were simply casual shoes.