The difference between a sprain and a fracture is that a fracture is a broken bone.
A fracture could be a partially broken bone or a completely broken bone.
A sprain is where you just have a ligament or tendon that has been stretched out, or maybe even torn.
The ligament or tendon with a sprain does not require a cast while a fracture such as a broken bone may require a cast to keep the bone in place and promote healing.
With a sprain you should be able to move your bones such as your foot, ankle, toes, fingers etc but with a fracture you may not be able to move those bones.
Your muscles control the bones and if you feel your bone and it feels like it's broken then it usually is.
Sprains don't usually require any medical attention and usually heal on their own but some fractures may require medical attention and a cast.