There were double density and high density disks. In theory the only difference was the quality of the magnetic material on the disk (older double density had iron oxide … newer and high density moved to Colbalt) and the high density disks had another hole in the casing so the drive could detect it.
The 880K / 720K etc difference was due to the different disk formats used (on double density disks) by Amiga and PC. The physical disk was the same.
Just like people used to turn over single sided 5 1/4 floppies and write on the other side - with newer double density disks you could just drill a hole in the casing and use as high density