mAh/g (milliamp-hours per gram) is a similar unit, but it’s missing the voltage term. We can do a little dimensional analysis here to translate between them. Power = Current * Voltage, so you’d multiply this (CurrentTime)/(Weight) value by the nominal voltage of the cell to get to (PowerTime)/(Weight). So it is essentially still a measurement of capacity, but in terms of current instead of power. Phone batteries are often specified in units of Current*Time (e.g. milliamp-hours), but I’m not sure why.