GM made a wide variety of transmissions in that era. What you have is a garden variety SM318 short tail-shaft Muncie. Earlier models had a long tail-shaft. There is also an overdrive offered along with some internal gear ratio differences. It doesn't really matter what they call it, if it has the same physical dimensions as yours it should work.
Fred


1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine