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?
The twist is the action. The sprain is the result, i.e. the end state of the action.
In English the two are often hard to distinguish. For example, consider the verb to score, as in He Shoots. He Scores. The equivalent French expression, lance et compte, could be translated literally as he shoots, and his shot counts. In French, the counting of the goal is the clearly the end state of action. However, in English, we use score to describe both the action of scoring and the end state of having scored.
There are pairs of words in English where the action and the end state have different origins, and by playing around with gerunds and participles, you can create similar problems, e.g. polish and shine, applied to furniture, shoes, floor tiles, etc. A shiny shoe is not necessarily a polished shoe.