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?
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.