These are in most cases referred to 'across the flats' (A/F) sizes, i.e. the size across the flats of the hexagon nut or bolt head, and can be either in Metric or Imperial fractional sizes.
The exception to this is the old British standard size of bolts (BSW or BSF) where the size given is invariably the diameter of the bolt and not the head. As the BSF is a finer thread than BSW, BSF bolts need a smaller head than BSW to reduce the possibility of stripping. Thus for example a 3/8 BSF bolt has only the same head size as that of a 5/16 BSW.