Strain, sprain as nouns can mean an injury to a part of the body through overstretching and as verbs to cause or to suffer such an injury to a part of the body.
Strain , the more general and less technical term, usually implies an injury to a body part or organ or to muscles as a result of overuse, overexercise, or overexertion or of overeffort (as in an attempt to regain one’s balance or to lift too heavy an object); the injury may range from a slight soreness or stiffness to a disabling damage; thus, eyestrain is a condition of the eye or of the muscles of the eye involving pain and fatigue such as occurs in those who do close work with their eyes or in those who suffer from uncorrected defects of vision; charley horse is a familiar term for a stiffness resulting from muscular strain in the arm or leg (as of an athlete).
But strain may specifically apply to an injury resulting from a wrench or twist and involving overstretching of muscles and ligaments and is then nearly interchangeable with, though typically suggesting less severe injury than, sprain which definitely implies an injury to a joint, usually as a result of a wrenching, with stretching or tearing of its ligaments, damage to the synovial membrane, swelling and pain, and disablement of the joint; thus, one may strain or sprain an ankle by a sudden slip that wrenches it.