The .380 ACP
aka 9mm Kurtz
or 9mm short
has a metric dimension of 9mmx17
and uses the same bullet as the 9mmx19
, a .355" diameter bullet
The most well known gun to use this cartridge is probably the Walther PPK which James Bond used for the longest part of his career after he decided to upgrade from the Browning .25 although nowadays James carries his Walther P99 in 9mmx19 (or possibly .40 S&W).
The .380 is a 9mm cartridge but unlike the 9mmx19 it is inherently subsonic in its normal loadings and thus is very appropriate for quiet work with a suppressor.
For people who are a bit recoil sensitive but want the higher capacity available in autoloading pistols, the .380 is an appropriate choice although it is indeed quite underpowered for a self defense round.
Why Colt called it .380 despite the fact it was .355" nobody knows.
Basically it is a smaller version of the .45 ACP dimensionally speaking.