Magnetic tape comprises a base film, upon which is coated a layer of iron oxide. Oxide of iron is sometimes, in other contexts, known as 'rust'. The oxide is bonded to the base film by a 'binder', which also lubricates the tape as it passes through the recorder. Other magnetic materials have been tried, but none suits analog audio recording better than iron, or more properly 'ferric' oxide.
There used to be several manufacturers of magnetic tape – Ampex (later called Quantegy) and BASF (later Emtec) were among the front-runners. But gradually most dropped out as the market shrank. Emtec tape is currently still available (and not just on eBay!).
Tape has been manufactured in a variety of widths. (It has also manufactured in a range of thicknesses – so-called 'long play' tape can fit a longer duration of recording on the same spool, at the expense of certain compromises.).
The widths in common use today are two-inch and half-inch.
Oddly enough, metrication doesn't seem to have reached analog tape and we tend to avoid talking about 50 mm and 12.5 mm. Other widths are still available, but they are only used in conjunction with 'legacy' equipment which is being used until it wears out and is scrapped, and for replay or remix of archive material.
Quarter-inch tape was in the past very widely used as the standard stereo medium, but there is now little point in using it as it has no advantages over other options that are available.
Two-inch tape is used on twenty-four track recorders. A twenty-four track recorder can record – obviously – twenty-four separate tracks across the width of the tape, thus keeping instruments separate until final mixdown to stereo.
Half-inch tape is used on stereo recorders for the final master.
The speed at which the tape travels is significant. Higher speeds are better for capturing high frequencies as the recorded wavelength is physically longer on the tape.
However, there are also irregularities (sometimes known as 'head bumps, or as 'woodles') in the bass end. The most common tape speed in professional use used to be 15 inches per second (38 cm/s), but these days it is more common to use 30 ips (76 cm/s), and not care about the massive cost in tape consumption!
At 30 ips, a standard reel of tape costing up to $150 lasts about sixteen minutes.
Hmm. Compare that with the cost of hard disk recording space these days…