translate (change location) in object more or edit mode? What is the difference between translating (i.e moving an object) in object mode and achieving the same thing by selecting all mesh elements in edit mode and then moving those? 

Why would one chose between the two methods?
In object mode, the object origin (the pink dot) moves as well. In edit mode, it doesn't.

The point is that if you want the origin to stay in a certain place, you could move all the elements in edit mode without affecting object origin location.