The grips are the same size for both the .32 and .380, but the guns are not the same. The early .380's have a larger magazine well and the .380 magazine won't fit in the .32 pistol. There are other differences, mainly the extractor. Unmarked original magazines are from the 1903-1908 period when there was only one caliber. After that, the magazines are marked with the caliber on the base plate.
The grip pattern was changed over time, so if possible get the style appropriate to the era of the gun. If you have enough of the original grips to determine that, fine. If not, check back and we will try to help you.