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I know of two wire gauges, in the UK we have Standard Wire Gauge (SWG), while the Americans use American(!) Wire Gauge (AWG).
The two are different but work the same way, a bigger number meaning a thinner wire.
If you can visualise an aviary for small finches and canaries the mesh will be made of 19SWG (around 18AWG) wire. The mesh on an aviary for parrots will be stronger - around 12SWG (close to 10AWG) wire.
You can Buy a Standard Wire Guage from the local hardware shop to measure the guage of your wire. Its basically small metal disc with holes or (nothces) of different sizes calibrated accoring to the standard.