Are Emperuman’s Hamsa avatar and Hyagriva avatar are one and same? This doubt arose due to the occurrence of of ‘hamsam’ in the Hyagriva Gayatri.

Emperuman’s Hamsa avatar and Hyagriva avatar are different. In the Hyagriva avatar, he retrieved the Vedas; in the Hamsa avatar he expounded on the meaning of the Vedas.
It is alright if the term ‘hamsam’ is found in Hyagriva Gayatri.