Here are the definitions of the words from Oxford Living Dictionaries:
sprain - wrench or twist the ligaments of (an ankle, wrist, or other joint) violently so as to cause pain and swelling but not dislocation.
‘Few dancers manage to perform without ever spraining an ankle.’
twist 1.6 - injure (a joint) by wrenching it.
‘he twisted his ankle trying to avoid his opponent's lunge’
What is the difference in meaning between these two terms? Is it the pain and swelling that is mentioned for sprain? Is there no pain or swelling in a twisted ankle?