Dimensionally very similar to the 9mmx21
the .38 Super like the many other .38
cartridges doesn't actually have a .38" sized bullet but one that is closer to that of the .355" 9mmx19 bullet
It is a high velocity round that Colt chambered some of their Government Model guns for.
There were initial problems of having cases split and ruin the slide and frame of the pistol because of the significantly higher pressures it generated over the more popular chambering for the Colt 1911 which is the .45 ACP of course.
Now with modern metallurgy and better manufacturing techniques the .38 Super has become a favorite among IPSC shooters. The smaller round allowed more to fit in the magazine which allowed more shots between reloads.
While not exotic, the .38 Super is not as common as the ubiquitous 9mmx19 as it is not an officially adopted cartridge of any armed force. It is mostly a sporting or competition cartrdge. I don't even know anybody who packs a gun in .38 Super for concealed carry.
If you want a light and fast autoloader cartridge for use with a high capacity pistol which you will use for concealed carry, go with the 9mm. Or better yet the .45 ACP.