For common speech, I agree with the accepted answer. However, I haven't seen anyone disambiguate the terms, and there is a difference.
"Floppy disk" covers all of the size and housing variants (8-inch, 5.25-inch, 3.5 inch). The disk is the round piece of thin flexible plastic inside the housing. It's "floppy" (i.e. flexible) as opposed to "hard" (as in "hard drive" or "hard disk drive").
"Diskette" is a portmanteu, combining "disk" and "cassette". The cassette is the hard plastic housing and its spring-loaded shutter.
Alternate technologies used hard disks inside cassettes too. Jaz disks are "hard diskettes" (a hard disk inside a cassette) but they're just referred to using the brand name.
disc
is only not used for magnetic media because the protective outer shell is non-removable. Intuitively, optical media is adisc
because it's visibly like a discus, while other kinds of media are adisk
because the most you can strip it down to without voiding the warranty isn't round. (i.e. It's a "disk" because you can't see the "disc(s)". A CD in a caddy is a disc because the caddy is conceptually a separate item. etc.)