  An alternative derivation of the known action-angle map of the standard open
Toda lattice is presented based on its identification as the natural map
between two gauge slices in the relevant symplectic reduction of the cotangent
bundle of $GL(n,{{\mathbb R}})$. This then permits to interpret Ruijsenaars'
action-angle duality for the Toda system in the same group-theoretic framework
which was established previously for Calogero type systems.
