  The third post-Newtonian approximation to the general relativistic dynamics
of two point-mass systems has been recently derived by two independent groups,
using different approaches, and different coordinate systems. By explicitly
exhibiting the map between the variables used in the two approaches we prove
their physical equivalence. Our map allows one to transfer all the known
results of the Arnowitt-Deser-Misner (ADM) approach to the harmonic-coordinates
one: in particular, it gives the value of the harmonic-coordinates Lagrangian,
and the expression of the ten conserved quantities associated to global
Poincar\'e invariance.
