.38 Auto is also known as .38 Rimless Smokeless. It's a John Browning design originally chambered in the Colt 1900 "Sight Safety". The case dimensions are virtually identical to the .38 Super, but the .38 Auto is much lower pressure.
Colt 1902 Pocket (Hammer)
top - .38 Rimless, Smokeless
.38 S&W is a shorter/fatter cartridge than a .38 S&W Special and the two are not interchangeable.