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 millimetre (American spelling millimeter) is a unit of length and is a multiple of the SI unit metre. It uses the symbol mm.
There are 1000 mm in 1 m and 10 mm in 1 cm. From this one can derive that there are 0.03937 in.
The millimetre is sometimes verbally abbreviated to 'mil' - which can cause confusion in the US as there is a unit there that means thousandth of an inch.