Title.
I know there are tools to set up a linux distro’s installer on a USB flashdrive. What I’m looking for is slightly different: I want to install a linux distro (a Debian derivative, but am still unsure which) on a USB hard drive, but I want to do it from a running system, rather that have to boot into installer mode.
The rationale is that this is the only active machine I have ATM. I guess this exists since that’s how “live distros” with installers even function in the first place, but I haven’t had much luck searching for information.


No, my goal is to set up a portable hard drive to use as an external system (to eg.: connect to machines to repair/diagnose them) without having to spend the 2+ hours of install and configure off my one working machine ATM.
Ah, okay. Then yes, as others have mentioned, it sounds like you want a portable linux install.
I keep around install USBs of both Arch Linux and Mint, as both boot into a live version of the distro, and I can either open a terminal to debug things, or arch-chroot into my arch install if I broke my bootloader or something.