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?
I was still a kid in the '80s, but basically grew up around (and in, sometimes), computer stores and computers. I don’t recall hearing this.