5.25" floppy disks are encased in a (usually black) soft protective case. The case exposes a thin sliver of the disk at the bottom. 5.25" floppy disks come in a few varieties:
SS SD floppy disks are single sided, single density.
SS DD floppy disks are single sided, double density.
DS DD floppy disks are double sided, double density.
DS HD floppy disks are double sided, high density.
Although the disks were sometimes double sided, the drives usually weren't, requiring you to eject and flip around the disk, much like a vinyl record or cassette tape.
3.5" floppy disks are encased in a (usually blue) hard protective caddy, but the disks themselves are still floppy. The thin sliver of disk at the bottom is protected by a sliding piece of metal. 3.5" floppy disks also come in a few varieties:
MF-2DD floppy disks are micro floppy, double sided, double density. They can hold up to about 1 MB of data, some of which gets lost to the entropy of the filesystem. They have a small square right-protect tab in the lower left corner (filled to allow writing, or showing a gap to protect against it), while the lower right corner is plain.
MF-2HD floppy disks are micro floppy, double sided, high density. They can hold up to about 2 MB of data pre-formatting. They have a small square right-protect tab in the lower left corner, and a permanent small square hole in lower right corner.
Quick Disks were a far less common format, used in a few samplers and MIDI sequencers (along with home computers, consoles, and word processors). Due to their obscurity, they're best avoided if possible.
Data storage formats: CD | Cassette tape | DAT | Floppy disk | MiniDisc