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 are is a unit of area and is a non-SI but metric unit with the symbol a.
It measures exactly 100m² which is the equivalent to 0.0247 acres.
The are is the principle unit for measuring the size of land across the world.