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AWG= American Wire Gauge also called B&S = Brown and Sharp
SWG= Standard Wire Gauge (British Imperial standard)
BG= Birmingham Gauge
It only makes a difference if you are ordering metal that needs to be certain thickness to make sure that you and the supplier are using the same scale (look at where 1/16" = 0.0625 falls on the different scales). A steel supplier may use one scale, a aluminum or stainless supplier another and a copper wire supplier still another.