According to Cambridge Dictionary, "sprain" means
an injury to a joint (= a place where two bones are connected) caused by a sudden movement
Do "a joint sprain" and "a joint displacement" mean the same thing?
Medical Sciences Stack Exchange is a question and answer site for professionals in medical and allied health fields, students of those professions, related academics, and others with a sound understanding of medicine and healthcare-related sciences. It only takes a minute to sign up.Sign up to join this community
You may be referring to "joint dislocation", instead of "joint displacement", which in my understanding would mean removal of the joint (at which point the two terms asked about obviously will not have anything in common).
As for sprain versus dislocation: In a sprain the bone endings making up the joint are moved out of their natural placement ("distorsion") with ligament injury ("sprain"), but do return to their natural placement afterwards (i. e. with the right configuration of communicating bone endings facing each other).
In a dislocation the moving out of place happens as well, but the bone endings do not move back to their natural configuration afterwards, meaning they luxated (joint dislocation is also called luxation).