The caliber is a unit of length based on the inch (imperial units) and uses the symbol cl.
It represents the internal diameter of a gun barrel and therefore more often than not, the size of the ammunition or round that gun requires to fire.
It is not always represented or converted exactly in inches so a table or "well-known" conversions are often used to depict measurements / ammo types instead.
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.