To follow up on this, here’s the interpretation I’d put on the concept of fast versus slow groupings of capital ships (battleships and battlecruisers) with other ships. The concept did exist in both WWI and WWII, but it took different forms.
In WWI (and the decade leading up to it), naval technology such as turbine engines and face-hardened armour, plus ship design philosophy in general, had progressed to the point where the dreadnought-type capital ship (uniform-caliber main battery in more than two twin turrets, good protection, and fairly high speed) had become feasible, but it had not progressed to the point where all three features (firepower, protection and speed) could be optimized at the same time. That would have to wait for WWII, when the true “fast battleship” type emerged. (The same thing happened with tanks, but with a one-war difference: in WWII, tanks could be optimized for two of three features, or have medium performance in all three areas, but it was only during the Cold War that technology allowed a tank to have excellent performance in all three areas.)
During WWI, technological limitations (plus the considerable influence of Admiral John Fisher, who was a visionary in both the good and the bad sense of the concept) led to the emergence of two varieties of dreadnought-type capital ships: the battleship and the battlecruiser. Basically, dreadnought battleships were reasonably fast (but not as fast as cruisers), and had both heavyweight firepower and heavyweight armour that allowed them to slug it out with anything afloat; the rule of thumb was that a balanced battleship design had “proportional” armour capable of dealing with an enemy ship carrying the same caliber of main guns as it itself carried. Battlecruisers were similar to dreadnought battleships (the British, in fact, tended to create a parallel class of battlecruiser for its respective battleship classes), but they carried fewer main gun turrets and had less armour so that they could achieve higher speed than a battleship; they were roughly as fast as a normal cruiser, considerably better-armed, and somewhat (but not always by much) better protected. Battlecruisers, according to British doctrine, were operated as part of what could be called “fast heavy scouting divisions,” in advance of the main formation of the more powerful but slower battleships. For a classic example of this, have a look at the two main British formations at the Battle of Jutland: Jellicoe’s slower battleship force, and Beatty’s faster battlecruiser force.
In WWII, the picture becomes more complicated. There were relatively few battlecruisers at that time, and they were a strange mixture of British and Japanese WWI hold-overs, weird German designs reflecting (or intended to cheat) treaty limitations, clear-headed French and Italian modern evolutions of the battlecruiser concept, plus the well-made but rather pointless American Alaska class (which the Americans denied were battlecruisers). To me, these odd ships muddy the picture more than anything else. In my opinion, the real fast-versus-slow capital ship distinction in WWII wasn’t between battlships and battlecruisers, it was between the modern 1930s- and 1940s-era “fast battleships” on the one hand and the surviving WWI-era battleships (some of hwich had been modernized between the wars) on the other hand. The classic example of that distinction can be found at Leyte Gulf, where the Americans assigned their old slow battleships (plus some escort carriers) to support the amphibious invasion directly (I think they were officially under McArthur’s command), and assigned their fast battleships and their fleet carriers (under Halsey) to fight the main Japanese fleet if it showed up. Halsey’s carrier pilots did take a substantial crack at the IJN during the Battle of the Sibuyan Sea (they sank the Musashi, notably), but Halsey later took the bait of a Japanese decoy operation and charged off to the north with his fast battleships and his fleet carriers to engage Japan’s remaining fleet carriers (which actually had few or no planes left aboard, and were simply meant to draw him away from Leyte Gulf). As a result, the Japanese surface-combat forces (in two groups, operating well away from the decoy force) had a clear shot at Leyte – and the American forces which ended up stopping them were, respectively, the US Navy’s older battleships at the Battle of Surigao Strait and a force of escort carriers and light surface-combat vessels at the Battle off Samar. In the latter engagement, the hopelessly outclassed (if you go by the raw ship types and numbers) Americans engaged the Japanese battle fleet so aggressively that the Japanese commander, Admiral Kurita, ended up retreating because, in his mind, the tiny American forces couldn’t possibly be attacking him so energetically unless they were expecting massive US Navy reinforcements to arrive at any moment. In fact, Admiral Sprague, the US commander on the spot, knew perfectly well that Halsey was nowhere near him; he dealt with a hopeless situation by going on the offensive because that was he was a leader in the tradition of WWI’s Ferdinand Foch (who at the Battle of the Marne reputedly signaled to his superiors: “My left flank is driven in; my centre is giving way; the situation is excellent: I attack!”)
