In the early fifties, Chrysler Corp decided to emulate GM and let each brand develop its own motor. So we had a Chrysler Hemi beginning in 1951, a DeSoto Hemi beginning in 52, and a Dodge Hemi beginning in 53, with less-expensive-to-produce poly versions of the Chrysler and Dodge coming 3-4 years later, followed by an all new Plymouth poly in 56. Completely different engine lines, with almost no interchangeable parts, but (as they grew) overlapping cubic inches - i.e., 331 Chrysler, 330 DeSoto and 325 Dodge, or 301 Chrysler and 301 Plymouth.
Chrysler realized having so many different engine lines was a dumb idea, and by the late fifties had consolidated into a corporate big block in low and raised deck versions, and a corporate small block - basically the Plymouth A and later LA. Different cubic inch versions of each, but basically only two V8 engine lines. (Plus sixes, of course.)
The 313 was a Canadian version of the Plymouth poly, the 315 was a Dodge motor.
Why Canadians got a 313 A motor while Americans got a 318 (and in 1956 Canadians got a 303 A motor, while Americans got a 277) - who knows? And why Canadian Plymouths (and 56 Fury) got a 303, while American Plymouths got a 301 (in 57) - who knows?
The above skips over the fact that for 2-3 years some Plymouths and DeSotos got Dodge poly motors, and some Canadian Dodges got Plymouth motors.
Simple, no?
A few years later, Plymouth had to fight like hell just to get a different cam for the Road Runner than the cam in the standard 383. It complicated production.