As OldChief says, the .38 S&W is slightly fatter and should not fit into a .38 Special chamber. There is a slight chance it may anyways (disregarding a modified cylinder; the Brits did that to some .38 Spl. M&P‘s in WW II).

However, back in the old days, when (at least according to the folks who look at the past with rose-colored glasses) old-fashioned craftsmanship was king, things actually didn‘t turn out with that much precision all the time, and you will find quite a few reports of older Smith & Wessons in .38 Special with chambers that will take a .38 S&W, even though they‘re not supposed to. In respect to the barrels, the difference of a few hundredths of an inch is irrelevant anyways, especially with lead bullets. So depending on what you have, you might just try