In the 1930s one of the big issues was that the police were "undergunned" by the gangsters. This seems to be a familiar theme and we heard it again in the '80's when the police all went to hi-cap "wondernines", then the .40 S&W, and lately assault rifles in the trunk. So S&W and Winchester developed the .357 Magnum revolver and this metal piercing loading for it in response in 1935.
Anyway, one of the law enforcement issues in 1935 was that the gangsters like Bonnie & Clyde and Machine Gun Kelly used automobiles as getaway vehicles and police shooting at the escaping car were unable to get it to stop using the standard .38 Special lead roundnose bullets that were issued. So a more powerful round, the .357 Mag, and specialty bullets, "metal piercing" were made available. Standard loads were also available as well. The .357 had about double the velocity and three times the energy of the .38 Special. This combination was intended, and actually would, stop a typical '20-'30's era car with a round in the engine block they say, but that eventually changed (although you could do your own tests on junk cars and let us know!). Of course the downside was that the .357 Magnum revolver (on the big N frame) from S&W was so expensive only the most well-heeled policeman and departments could ever hope to own one until the 1950's. I don't know the exact bullet construction, but would assume that is just had a very heavy jacket and hard lead core, combined with its unique shape. I would think that box you seen would almost be a collector item now.
Cartridges Of The World notes that "During the Korean conflict it was found to be very effective against the body armor used by the Communist forces."
You might be interested to know that Colt introduced the .38 Super in its 1911A1 for much the same reason in 1929. In 1930 S&W had the N Frame (.44 Mag size) also chambered for a more powerful .38 Special loading - the .38-44 Heavy Duty that used a 158-gr bullet at nearly 1,150 fps. The barrel was still marked "38 S&W. Special CTG" but brass had a "38-44 SPL" headstamp. This was a precursor to the .357 Mag. There might even have been a metal piercing loading for this as well, but I don't know for sure.
If you have a .357 Magnum revolver you can duplicate this load with 11 to 11.5 grains of 2400 with RN-FP lead bullets in the 150-165 range in a .38 Special case. DON'T try this in a standard or +P rated .38 revolver. See Oct. 2007 Handloader magazine for more details.
The stuff is legal, but discontinued and considered obsolete.