They use a similar steel case form to the Commodore 9060/9090 hard disk drives, and use the parallel IEEE-488 interface common to Commodore PET/CBM computers.
Essentially, both models are a single-drive version of the Commodore 2040/4040 units.
The Commodore 2031LP is functionally the same as the 2031, but used the lower-profile tan case of the second version of the Commodore 1540 floppy disk drive intended for home computer use.
These drive models use a single-density, single-side floppy data storage format similar to that used by the Commodore 1540 & Commodore 1541 drives, but with a slightly different data marker indicating which model originally formatted the disk.
A difference of one extra 'header' byte is what causes this write incompatibility.