“-Ette” is a common diminutive used to imply that something is a smaller version of something else. Like many things, we nicked it from the French.

Cigarette, a little cigar. Featurette, a short feature. Novelette, a miniature novel. Etc.

So, diskette, a little disk. Quite separate from the ones spinning in your company’s mainframe at the time. Those ones were two feet in diameter locked in a steel cabinet that weighs two tons. This one can fit in your shirt pocket. You get the idea.