While the bullet size for the Browning developed .38 ACP and the 9.mm are essentially the same, the cases are different the 9mm case mouth is 9.56 mm in diameter, the .38 is 9.8. The 9mm case diameter at the base is 9.93 and the .38 is straight walled at 9.8. But the most important difference is the case length. The 9mm is 29.99 mm long while the .38 is 22.90 mm.
So the .38 would probably fit the 9mm magazine but it would not feed or probably fire properly.