3.5" floppy disks, in the transition from 720K to 1.44M, changed the actual coating to a different compound that was magnetically 'stiffer'. This was necessary to support the higher density, but meant the old disks could not support the new high-density format even if used in a new drive. A more subtle and much nastier problem: if you formatted a new disk in an old drive, everything would seem fine, but the information would not have been recorded strongly enough, and might fade over the next few days.
5.25" floppies made several format transitions that together accomplished an order of magnitude capacity increase until the final 1.2M format. Did any of these transitions involve a similar change in the actual coating? Or did the disks themselves stay interchangeable apart from issues of hard versus soft sectors?