A wight might probably be simply best defined as an undead shaman or wizard king, whose hollow eye sockets glow with an eldritch light whilst their skeletal remains are kept animated by means of powerful necromantic magic.
Wights need not necessarily be confined to the role of undead necromancers though, as they may also be encountered in the form of some ancient warrior, whose soul similarly inhabits its own former or another's, corpsing husk.
As the previous respondents have already stated, a ghost is simply an immaterial entity, perhaps aware but just as easily unaware, of its own nature, surroundings or concept of time.
It might simply just be replaying an event from its material life where great emotions were experienced. These events might be replayed over and over in a never ending loop.
Whereas a wraith I feel, is an entity that whilst not of material substance, is driven by a powerful purpose.
This is an ethereal being of pure malice whose actions are governed usually by its own thoughts.
Such a being exists to perform a very specific task/tasks and its existence is maintained until such tasks have been fulfilled.