“Cartridge brass” is a (generally) standard alloy of 70% copper and 30% zinc. That doesn’t mean all cartridge makers use exactly that alloy. Varying the proportions gives the alloy different characteristics - mainly on a spectrum from soft and springy (more copper) to hard and tough (more zinc). Other components like tin tweak the metal further for specific (and probably very arcane) reasons.
The Accurate Shooter article gives a couple of excellent examples of how different the alloys can be. With that said, both Winchester and S&B use an alloy that’s pretty close to the classic cartridge brass. This alloy was developed (empirically and long ago) to provide a very good compromise between springiness and the ability to harden parts of the case sufficiently to get the case to do what it needs to do.
I think that the variations between different alloys may be why annealing some cases leaves more or less of a discoloration - according to the AS article, some alloy ingredients change the visual characteristics of the brass, and might affect the degree of color change seen with even very precise annealing processes.