How naval treaties classified warships

Did naval treaties distinguish destroyers, cruisers, and battleships by displacement, gun size, or both?

Both, but displacement was the primary classification and gun calibre was secondary.

The treaty categories did not rely on a single physical feature. Displacement supplied the primary boundary between major warship types. Gun calibre then acted as a secondary definition, separating cruiser and battleship armament even when unusual weapons sat awkwardly between them. A destroyer that exceeded its allowed tonnage could therefore become a cruiser for treaty purposes regardless of its intended label.