Something amiss there. The .38 Short Colt, even with the heeled bullet, should have chambered in the .38 S&W cylinder.
This is not to doubt the truth of your experience.
The original. heeled, bullet for the Short Colt was .360 - .361", pretty much the same as the .38 S&W (.361-.362), certainly it should not have been larger.
The .38 Short Colt was the parent case for the .38 Long Colt, and then the .38 S&W Special, and ultimately the .357 Magnum as it has an interior diameter of .357.
The interior diameter of the .38 S&W is .361-.362"
Pete