All the '46 running boards i've ever seen that didn't have a bed originally end right about the back of the cab, and are nicely rolled over, not just cut off.
My guess is your 3/4 ton truck started life as a pickup, and the bed probably went to hell, and somebody decided to just pull it off and put a stakebed on it.
To find out for sure what your truck started out as from the factory, hook us up with the serial number found on the plate attached to the firewall on the passenger side and we can look it up.