Some points being missed in the last posts ..
(a) S doesn't matter .. it's just a quantity necessary to make the units right in a non-dimensional parameter and is for OEM convenience .. at the end of the day CL is just a number and, as you have observed by inference, comparison of CL is not normally the mode of rating competing aircraft. Having said that, most OEM use similar (if not identical) definitions so notional comparisons are not unreasonable.
(b) the OEM sells aircraft based not on absolute CL values but hard dollar quantities which involve aerodynamic parameters .. eg take off and landing distances, fuel burn, econ speeds, etc. The customer out there in the marketplace really isn't too fussed about what CL values the OEM plays with ...