How is a fracture different from a hairline fracture in the ankle?

No difference: A "hairline fracture" is a layman's term for a non-displaced fracture (a break in the bone, but the bone has not move out of position at all). All hairline fractures are fractures, but not all fractures are hairline fractures, as fractures are often times displaced due to the force of the injury and/or due to the muscle pull of the surrounding muscles.

Fracture: A fracture is a fracture both would be treated by immobilization unless there is a through and through fracture with displacement than surgery might be necessary.