In almost all cases it'll be the same situation. The boot manager is pointing the wrong way. You added the entry to the 100GB drive when you (or whatever Mint uses to install) ran grub-install. You also have an existing entry for the OS on the 128GB drive.
The only way it would have worked seamlessly is if you plugged the 128GB drive into the same connection that the 100GB drive was on AND both the original OS and Mint both use grub AND install it in the same location.
It's an easy fix once you know what to look for (just run efibootmgr --unicode and you'll see the boot entries).
Apparently my 128GB is a SATA M2.
