The foot is a unit of length in the imperial unit system and uses the symbol ft.
One foot is exactly equal to 12 inches. It is also exactly equal to 0.3048m. One yard is comprised of three feet.
The foot is just behind the metre in terms of widespread use due to its previous popularity. The US is the only developed country that still uses the foot in preference to the metre.
The UK still uses feet to express human height more than metres.
The em is a unit of length in the field of typography and uses the symbol em.
It is a "relative" unit and equals the currently specified point size. For example, 1 em in a 24-point typeface is equal to 24 points. This allows a typographer to specify text size relative to a base figure.
In metal type, the em was equal to the line height of the metal body. This meant the physical size of the letter could not exceed the em. In digital type, the em is a grid of arbitrary resolution so can be scaled to any point size for screen or print.