In the 50's and 60's, thousands of surplus S&W M&P revolvers chambered for .38 S&W were rechambered for .38 Special. At the time, there was a lot of alarm and concern about the practice. In fact, there seems never to have been any problem except that the cases swelled a bit more than normal and didn't last as long when reloaded. Accuracy was good in spite of the difference in bullet diameter.
AFAIK, there were no reports of any damage to revolvers or to shooters. But note that the M&P had been designed for the .38 Special; the above might not be true for other guns made for the .38 S&W. Needless to say, none of the old guns, even the M&P, should be fired with +P or +P+ loads.
Jim