The barn is a unit of area and is used in particle physics with the symbol b.
It represents approximately the area of the cross-section of a uraneum nucleus, so is very small compared to most other recognised units of area.
It is also used to measure the interaction of a nucleus with an electric field gradient in nuclear quadrupole and magnetic resonance.
The square metre is a unit of area and is an SI derived unit with the symbol m².
It was introduced in 1954 when the International System of Units was established and was derived directly from one of the original 6 base units - the metre (m).
It can be prefixed with any of the SI symbols that multiply it up or down such as km² (square kilometre) or µm2 (square micrometre). It is the most commonly used unit of area and is recognised all over the world.