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1541, 1581, and variations
Commodore 64 disks come in two varieties: GCR, which are the overwhelming majority; and MFM, only used on the 1571 and 1581. The latter were (as far as I can tell) standard IBM PC format disks with a slightly odd sector count.
The GCR disks are much more interesting. They could store 170kB on a single-sided disk (although later drives were double-sided), using a proprietary encoding and record scheme; like Apple Macintosh disks they stored varying numbers of sectors per track to make the most of the physical disk area, although unlike them they did it by changing the bitrate rather than adjusting the motor speed.
The drives were also intelligent and ran DOS on a CPU inside them. The computer itself knew nothing about file systems. You could even upload programs onto the drive and run them there, allowing all sorts of custom disk formats, although this was mostly used to compensate for the cripplingly slow connection to the computer of 300 bytes per second (!). (The drive itself could transfer data reasonably quickly.)
A standard 1541 disk has 35 tracks of 17 to 21 sectors, each 256 bytes long (sometimes 40 tracks).
A standard 1581 disk has 80 tracks and two sides, each with 10 sectors, 512 bytes long.
A CMD FD2000 disk (a popular third-party Commodore disk drive)
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References
- Ruud's Commodore Site: 1541: documentation on the 1541 disk format.