Representation of space time in GTR

Blackforest

It is not a homework but a general question concerning the nature of our spacetime in physics. Perhaps the question will appear to be not relevant and perhaps it is not exactly the good place to post it here.

Is there a difference between the two following way of doing: (a) in treating the space time of general relativity as an affine set (a set of points) and (b) in treating it as a field of tetrads ? Does the complicated vectorial nature of the tetrad concept bring some new informations concerning the texture of that space time?