vThe difference is in the barrel hood tang - the part that sticks out at the top rear of the barrel and has the loaded chamber indicator hole.

A 40 barrel has a wider tang than a 9mm. A 9mm conversion barrel has the wider tang to ensure proper lockup in the slide.

Post #11 on this thread has a picture that shows the difference:
Stock 9mm Barrel vs Storm Lake 9mm Conversion Barrel