The 125s had the short large diameter pump (from memory maybe an inch tall and inch in diameter.
Both the 1365s and the 150s have the long slender pump (again from memory maybe 2 1/2 inches tall by 5/8 inch diameter).
Repeat: both of the above dimensions are from memory, and are probably close but not exact. They do, however show that one pump is short and stubby, the other longer and slender.
As to the 150 -> replacing the 136s:
When we still had time to restore carburetors, we would always suggest if a customer wanted a 136s to actually use the 150s. The 150s was a factory service replacement, so both Carter and Chevrolet agree with this statement

The major difference from the 136s to the 150s is a slightly larger main venturi (again memory 7/8 -> 15/16) in the 150s; so the airflow in the 150s is slightly higher. Of course, this requires different jetting.
Externally, I believe there is no difference in the 150s/136s (unless you have one with the red cardboard tag

).
One other comment which is strictly opinion:
NONE of these carbs are really GOOD carbs; however, one that is restored is beautiful! Today, if one is planning to put some miles on the vehicle, there are a number of aftermarket carburetors which will provide better driveability, more power, better fuel economy, and much better reliability (plus they are less expensive!).
Jon.