A bit like 'fear' and 'Love.' Some still feel that we should fear God, but more and more are associating with the word 'Love.'
Contract seems more base, more business-like. It is an agreement which is binding. A Covenant usually reaches up to something, like the Divine and is not binding. 'Do this or else.' Covenants can also be legally applied to Will's and other matters, but generally it is a higher, more comforting word in relationship to the Divine.