Compared to 5.25" and 8" floppy disks, the 3.5" weren’t very floppy. They didn’t bend that easily, were stiff compared to the older formats.
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Generally, the term floppy disk persisted, even though later style floppy disks have a rigid case around an internal floppy disk.
Where there people who refused to call 3.5" floppy disks floppy disks because they weren’t floppy enough?
The disc inside is still round though. Did you never crack one open to see?
Of course I did. OP is asking if our description matched the inside or the outside, I’m giving further evidence that the (rigid, square) casing didn’t affect that description.