The #358311 was the second design from Ideal made for the 38 S&W Special load. The #358250 was the black powder bullet that held almost twice as much lube and could compress the black powder when loaded, it was so long. The new #358311 took up less case room and was very accurate. Even when the Colt 38 Special bullet (#358416 RNFP) was introduced in the 1920's it could not displace the #358311.
From 1890's to the 1910's was a great time to a 38. Lots of research for the S&W, New Police, Army, S&W special and Colt Special. Because they were so much easier and cheaper to shoot than the 44's. So both target and field shooters flocked to the .38's.