"As to the metal penetrating bullets made in the 'Twenties and 'Thirties, maybe even into the 'Forties, these bullets had a hardened steel core under the jacket."
Over the years there were numerous variations -- from soft lead to apparently some sort of zinc based white metal.
I've never heard, however, of any of them having penetrators in them.
Remember, even with the cars of the time, we're not talking armor plate, we're talking relatively thin (certainly thicker than today, though) mild sheet steel.
See here for some more information:
There are also a number of threads online by people who have sectioned these bullets and have also found either dead soft lead or some type of composition metal.
AH! Excellent. Here's a page with some very nicely done section bullets, including a number of the kinds that we're talking about mixed in with much later versions...
Last picture, first row, last section is a .38 Spl. Western Olin. It has a MUCH thicker nose jacket profile.