The Powermatics and Hydra-Matics were different transmissions made by different GM transmission divisions/plants.

Yes, the Allison 6-speed Powermatic (Torqmatic) was available in 1956 GMC and Chevrolet trucks.
Here is a 1956 newspaper article describing the availability of both transmissions in 1956 (Powermatic available in the Chevrolet 2-ton group)

1955 Twin Hydra-Matic (a Supplement Manual was available in 1956)

1957-1959 Hydra-Matic manual

1956 Powermatic manual cover

1958 Powermatic manual cover ( complete manual )