What is the main difference between a twisted ankle and a broken ankle?

Ligaments vs Bone. A twisted, or sprained ankle is an injury to one or more of the ligaments that connect the bones of the lower leg and foot. A broken ankle is a fracture of one or more of the bones of the lower leg. One can usually recover from a sprain within a few weeks, while a fracture usually takes about 8-12 weeks to heal.
Injury. A 'twisted' ankle really just describes the mechanism of injury. An ankle sprain usually refers to injury of the ankle ligaments whereas a 'broken' ankle describes a fracture to the bone. These injuries can be treated nonoperatively or surgically depending on the damage.