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Running shoes can be used as a gym shoe if treadmill walking or running is making up the majority of your workout. But weightlifting shoe won't.
Weightlifting shoes have a raised heel, usually . 75-1” in height, made of hard, non-compressible material. Allow you to safely lift heavier load
When you're lifting, a rigid sole is best so that the heels can drive into the floor during exercises such as squats and deadlifts.