The .38 the military adopted as it's main pistol caliber was the .38 Long Colt, which was black powder and due to the design of the bullet tended to exit the barrel undersized
.38 Special has a pretty long history in the US military, with various revolvers chambered in it being substitute standards (off the top of my head, the US military has issued S&W .38 Hand Ejector, the S&W Victory, the S&W Model 10, Colt Commando snubs, Colt AND S&W patten M13 Aircrewmans, Ruger Service Sixes, S&W Model 12's, and S&W Model 15's). Also a loooooot of people that privately purchased sidearms (when one could get such a thing allowed) bought .38's, mostly Colt and S&W
https://www.americanrifleman.org/art...ary-revolvers/
http://smith-wessonforum.com/s-w-rev...w-vietnam.html