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No. You can sprain both wrists and ankles without twisting them. However, if you twist your wrist (deliberately), you will see that you forearm usually goes with it, so there's no injury. Most wrist sprains are not caused by twisting.
Note also that 'sprain' or 'strain' is a pathological diagnosis; 'twist' is the method of injury - "twisted ankle" is not a formal medical diagnosis.