Most commonly general practitioner will diagnose wrist and hand injuries as either carpal tunnel, dupuytren's contractures or de quervain's syndrome. Again these conditions are not a pure diagnosis to which you would treat, they are generally “pigeonhole” terms to which other conditions co-exist.
As the hand is a functional tool is must remain as mobile as possible, if it is functionally it will develop the strength with use in the way required. As with the lower leg, the hand can be affected by neurological issues because of its distance from the central nervous structures, the more obstacles a nerve has to pass the higher the likelihood that it will meet resistance. So a good assessment of hand function would always involve a review of the nerve structures.