For simplicity sake, say you have a good old ii-V-I in C. If the bass player is playing the roots, D to G to C, then on piano I won't want to play the chords starting on those same roots. So I'd maybe play FACE, FABE, then EABD.
you have to specify which octave. chords behave differently texturally depending on which octave, especially when we're talking about arranging which instruments play what