Mint 20.1 installation media is stamped correctly on the USB stick (presumably).
It doesn't see the HDD or the SSD, both 1TB, but they see the larger 4TB hard drive.
What do the HD and 1TB SSD have in common, other than capacity, of course?
One hypothesis would be the settings of the SATA port where these devices are connected, assuming it is the same SATA port.
Try connecting the device (HD or SSD) to another port or review the settings in the machine's "setup".
Is there RST in play?
In fact, it doesn't make sense for a currently supported Linux distribution not to recognize a simple HD or SSD.