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 nanometre is a unit of length and is a multiple of the SI unit metre. It uses the symbol nm.
1 nm is equal to one one-billionth of a metre. (Nano is the prefix for one billionth). It is used to express dimensions on an atomic scale for example a helium atom has a radius of approximately 0.03nm.
The nanometre was previously known as the millimicrometre (or the millimicron).