The Lord usually talks about shama and dama both together.
*sarva-dvArANi samyamya mano hRRidi nirudhya ca* (VIII – 12) :
Here ‘sarva-dvArANi samyamya’ (damming all gates) is ‘dama’; ‘mano hRRidi nirudhya’ (fixing the mind in the heart) is ‘shama’.
The dvAras are the gates; these gates are the indriyas, namely, ears, nose and mouth – in which the gates are visible and explicit; and the skin, in which the gates are not visible, but we know every hair on the skin is only a gate-like equipment, though invisible; and finally the eyes, which we know is just a fixture in one of the openings of the skull and further light passes through the eyes and creates all the images that we see.
So the controlling of these five gates is nothing but the dama that controls the senses. And the process of controlling the mind and stabilising it in the Atman is the shama described in “mano hRRidi nirudhya”.
“bhavanti bhAvA bhUtAnAM matta eva pRRithak-vidhAH” – All the different attitudes of the beings emanate from Me, says the Lord.
And then He gives a list of the highest among them: (X – 4, 5) Intellect, wisdom, non-delusion, forgiveness, truth, self- restraint (dama) , calmness (shama), ... . And when he makes a list of all divine qualities in the 16th chapter, he includes both dama and shama in “dAnaM damashca” and “tyAgaH shAntiH” (XVI – 1, 2).
As I have already mentioned, what is obtained by shama is shAnti (Peace) and what is obtained by dama is ‘dAnti’.