Hi Dexter, sorry to butt in. I think you're confused a bit about your drives both being "named" or "labeled" as /dev/sda1. That is not quite the case. It is happening because you only allow them to be plugged in one-at-a-time. When Linux boots up, it "identifies" the drives that are installed... by a combination of auto-detect and by configuration files like fstab and mtab.
Physical hard drives are typically identifed as sda, sdb, sdc, etc. Partitions are identified with a number after the drive identity, so sda1 is the 1st partition on the 1st hard drive, and sdb3 is the 3rd partition on the 2nd hard drive.
Because you made both of your drives bootable with Linux Mint, you would probably need to use your BIOS Boot Menu to pick which one to boot from if you left them both connected when starting the computer. Your BIOS Boot Menu would also identify the drive, probably by brand name, so you would know which one your booting. Then, when you examine your disk arrangement, you will most likely find that the boot drive is /dev/sda1 as you've seen before, but the other one will be different.... maybe /dev/sdb, but it can also be further down the alphabet (especially if it is an external drive connected by USB).... perhaps as far as /dev/sdf or /dev/sdg.
You can, in fact, assign a drive "label" to each drive (like "STORGE" or "MEDIA" etc). A utility called Gparted can do this, and there are other methods as well. Drive labels are also helpful, but Linux does not usually create them automatically on hard drives. It is more common when creating a bootable Linux USB flash drive that it will have a drive label assigned to it.
So, if you leave both drives connected, and you boot on the SSD.... and you are SURE you booted on the SSD.... then you can use Gparted to erase all of the partitions on the 2TB drive, label it as "STORAGE" if you want, and then format it so that it is clean and ready to use. If this drive will be used in a portable USB enclosure and shared with Windows computers, then you would want to format it as NTFS so both Linux and Windows can use it. Windows cannot use the various Linux file systems (and FAT32 is too old and outdated to use on a large drive like that).
Cheers