Why protected and armored cruisers do not map neatly onto treaty cruisers

Did the same logic that favored light or heavy cruisers also govern the choice between protected and armored cruisers?

Only broadly. The earlier ships belonged to a different machinery and fire-control paradigm, so their armor and armament tradeoffs cannot be mapped directly onto treaty-era cruiser categories.

The two comparisons share only a broad resemblance because machinery, engagement range, and fire control changed between the periods. Protected and armored cruisers operated before mature centralized fire control, often with guns under local control and much shorter effective ranges. Later light-versus-heavy cruiser choices involved the shell weight that a battery could deliver within a particular engagement window. A 5.25-inch gun is cited as theoretically firing faster than a 6-inch gun and therefore potentially delivering greater shell weight over that interval. Mechanical loading limits and hand loading both affect that calculation. The comparison remains approximate because the two generations cannot be balanced on the same technological assumptions.