All disk storage is basically the same; a circular platter is coated with a magnetic coating. A read/write head is used to read and write data on the disk as the disk is rotated underneath (or above) it, by magnetizing the particles in one of two directions.
In most disks, the platter rotates at high speed, and the heads are shaped to ride on a thin film of air at a very low altitude above the surface of the platter (a small spacing is required to maximize the density of the data on the platter; the smaller the spacing, the more densely the information can be written).
With the head at a fixed position, it writes a circular track. Some early disks had a separate head for each track; such disks were known as fixed-head disks.
For most disks, a head is shared between tracks; a separate mechanism is used to move the head in and out, a process known as seeking. The drive can write data on many tracks, each at a fixed distance from its neighbours. This is mechanically more complex, but uses fewer components overall.
Many disks have more than one platter, each with its own read-write heads (usually two, one for each surface), and the collection of tracks at a given offset is referred to as a cylinder.
A complete track usually contains more data than can easily be read and written as an un-divided unit, and so tracks are usually divided divided up into a number of sectors or blocks. This division may be purely logical, and indicated in the magnetic pattern written to the disk, or there may be actual physical means of indicating where each block is. There is also an intermediate (used in most floppy disks), where there is a physical mark to indicate the start of the track, but the sectors are logical.
Most early disk drives used packs, a group of one or more platters which could be installed or removed in a drive, in a process called mounting a pack. So a system could have multiple packs (for backup purposes, or for infrequently needed data) which could be stored until needed.
Initially, all disks used large metal platters (usually aluminium), complex mechanisms to move the heads in and out at high speed (to reduce seek times), and were generally fairly expensive.
In the late 1960's, IBM developed a new form of disk, the floppy drive, which used instead a 'platter' of mylar (a stiff plastic); this was much cheaper, but at significantly lower performance. In these drives, the disk rotates much more slowly, and the head makes contact with the surface.
The rotating substrate - not referred to as platters, but called the 'magnetic medium' was carried in a stiff plastic envelope, with a thin felt layer on the inside (to keep the medium clean). The entire assembly is usually referred to as a floppy disk (or 'floppy' for short).
The first floppies were 8 inches in diameter; later they were produced in 5-1/4 inch, and finally 3-1/2 inch sizes (the latter in rigid plastic containers).
More recently, to increase the amount of information stored on a drive, most disk drives are now sealed. The disks in modern personal computers are generally referred to as hard drives (to distinguish them from the floppy drives which were all the earliest PC's were equipped with).