The astronomical unit is a unit of length and is used in the Astronomical system of units and denoted by the symbol au.
It represents the average distance between the Earth and the Sun which is approximately 150 million kilometres (or 93 million miles).
It's used mostly to express distances within our Solar System.
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.