When battleships paired with destroyers and carriers with cruisers

Did battleships naturally operate with destroyers while carriers operated with cruisers?

Often in the interwar period, but the pattern became less fixed in wartime and postwar fleet destroyers had to work with every major force type.

The answer sees a good case for battleship-destroyer and carrier-cruiser groupings in the 1920s and 1930s. By the Second World War, the answer depends on which kind of destroyer and mission is under discussion. After the war, large fleet destroyers increasingly absorbed duties that connected them with every major force element. The exchange shows why ship-type relationships must be tied to a period rather than treated as permanent fleet rules.