How do you tell the difference between a sprained or twisted ankle?

Sprain vs twisted: I believe they are interchangeable.

Same thing: Twisting ones’ ankle can lead to a sprained ankle. Often times, this results in a ligamentous injuries which may lead to ankle swelling, pain, and possibly instability.

Twist = Sprain: In most cases people tend to use the terms "sprained" and "twisted" synonomously when describing ankle injuries. However, it is important to point out that in most cases a sprain (ligament damage) usually comes from a twisting mechanism (also known as inversion or eversion) of the ankle.