I thought we called them gymshoes, but it appears not (was life so complicated?):
“Gym shoes are performance- oriented athletic shoes built for training and indoor workouts, featuring multidirectional grip and stability. Plimsolls are simple, flat-soled canvas shoes with rubber rims, typically used for casual wear or light P.E. Tennis shoes are sport-specific court shoes designed to handle side-to-side movements and sudden stops.”