ABW (Alcohol by Weight) expresses a beverage's alcohol content as a percentage of its total weight rather than its total volume — the same underlying fact about a beer's strength, described through a different unit, and one that reads a noticeably different number for the exact same beer.
Why the two numbers never match
Because ethanol is less dense than water, a given volume of alcohol weighs less than the same volume of water would — which means ABW always reads lower than ABV for identical beer, typically by a factor of roughly 1.25 (an ABV figure divided by about 1.25 gives a rough ABW estimate). A beer at 5% ABV is close to 4% ABW, not the same number expressed differently by coincidence.
Where this actually shows up for a homebrewer
Most American beer labeling and homebrewing convention defaults to ABV, so ABW mostly matters when reading regulatory or legal documents (some older or state-specific alcohol regulations were historically written in ABW terms) or comparing figures against sources that default to the weight-based convention instead — worth a quick mental conversion rather than assuming the two numbers are interchangeable, since treating a 5% ABW figure as if it meant ABV overstates the beer's actual strength.