The -ette in cassette and diskette is a diminutive suffix. Cassette means little box. Casse is French for box. And thus Diskette means little disk, not disk in a protective case. IBM introduced the term to mean floppy disks smaller than their 8” floppy disks
Disk comes from the Greek word Diskos. And Disc from the French word Disque.
Diskette means little disk. Floppy disks existed before diskettes.
Diskette comes from cassette which had been used in photography long before describing tapes and just meant that it had a built in protective case.
The -ette in cassette and diskette is a diminutive suffix. Cassette means little box. Casse is French for box. And thus Diskette means little disk, not disk in a protective case. IBM introduced the term to mean floppy disks smaller than their 8” floppy disks
https://www.etymonline.com/word/cassette
https://www.etymonline.com/word/diskette