Gym trainers have very different features compared to running footwear. Gym trainers aim to provide the support for all round traction rather than the simple linear motion of running. This is necessary for lateral movement during workouts and fitness classes.
Gym footwear tends to have a breathable upper material and a secure lacing system to keep your foot stable and to help give support to your ankles. They offer more forefront flexibility to increase stability whilst still allowing for agility.