So when we look at how the two fleets fought, it is important to look at how they INTENDED to fight, and then how circumstances changed that.

SO first we need to consider the restrictions that both sides were under, Japan was working with a relatively tiny industrial base, whilst the US had to be able to respond effectively and in force on two oceans and across half the world. And both sides had signed the Washington Naval Treaty, fixing the number of capitol ships, definitions of cruisers, and various tonnage rates for the major fleets. But basically it gave the US (and UK) a 5:3 advantage over Japan. That meant Japan needed to squeeze every ounce of offense out of her ships. and in large part both sides adopted rival plans to control the Pacific. The US under what began as War Plan ORANGE, sought to essentially write off her forward holdings like Guam and the Philippines, grow and mobilize, then gradually seize forward bases and places to serve as harbors, preferably where the enemy was weak, and then hopefully destroy most of the IJN in a large single or series of Mahanian decisive battles, blockade the Home Islands and starve Japan into defeat, that should sound familiar as it formed essentially the basis for the Pacific War,the USN had been planning to fight Japan for 40 years and in most major respects got it right.

Japan meanwhile sought to fortify a series of outer islands, and bleed the USN before closing for a decisive battle to cause such loses as to force negotiations. In particular air craft were thought potentially useful (they were for a good deal longer seen mostly as Scouts in the USN), submarines focused on hunting warships, and her light ships. Japanese Cruisers and Destroyers trained extensively for night combat and int he use of massed long range torpedo attacks. Very much building on the legacy of their smashing victory over the Russians in 1905. But underestimating the ability and willingness of the US to absorb casualties, and of the importance of avoiding great losses themselves.

Now for some definitions and brief mention of usage. You are mostly right on your understandings.

For both sides in 1941 as in decades past the primary way that the war would be won was by the Battleships of one side sinking the others. The Pacific Fleet for instance was divided into 2 groups the Battle Force and Scouting Force. The Battle Force consisted of the Battleships divided into Squadrons, with a handful of light cruisers (light meaning armed with 6in guns heavies had 8in guns) and destroyers to protect from submarines, and enemy light ships as an outer screen. The Scouting Force was made up of small squadrons of cruisers and destroyers along with the carriers, its main goal being to operate in partnership with the Battle Force and find the enemy, then harry it, and protect the Battle Line from surprises.

We can see here in the late 20's the fleet anchored in Guantanamo Bay for Summer drills, the large battleships anchored in back, with the early carrier Langley, then the cruisers around them, and destroyers farther out. http://i.imgur.com/Mgxuo66.jpg

Then here we have the US Battle Line drilling in the 30's, the US had built 5 successive classes of BB's The Standard Types, who all had about the same speed and similar capabilities, so the could all operate together. http://i.imgur.com/xW6rNCG.jpg

So both sides in large parts were preparing to fight a battle in large respects similar to the way naval battles had been fought for 400 years right up till Tsushima, and Jutland. Two opposing lines of heavy ships with a screen of small ships slowly close through the enemy screen, and hammer away.

But by the late 30's several things changed, one is carriers became more effective, larger and could carry large planes with larger loads of weapons. The other is the breakdown in the naval treaty system meaning new construction took off particularly in the US.

Larger carriers meant planes could carry a torpedo our 2-300 miles and return, making the Carrier an effective first strike weapon, but the Carriers were faster than the Battleships, so no heavy units could really back them up or provide a fast heavy 1-2 punch. So the new generation of "fast battleships" evolved, adopting lines of thought from ideas such as the battle-cruiser, and more traditional designs, typified by the Iowa Class. Meanwhile the IJN simply didnt have the resources to build many new ships having not built new BB's and only a handful of carriers since the 20's. So the went BIG, building a sprinkling of new carriers of larger design, but also seeking to build ships so powerful that they would make up for the number imbalance of the Battle line, hence the Yamato was born.

So come December 7th the entire Battle Force is basically taken off the board, but the Scouting Force, the form of 3 Carrier Groups with more on the way, survives. And as the IJN demonstrated modern aircraft were plenty powerful if used smartly. Thus the US had nothing but the carriers to work with and protected them with great care. The first fast battleships were still jsut being placed ins service, but unfortunately the Navy just couldnt keep the fueled and forward. There was a great initial shortage of oilers and fuel ships to keep the Navy sailing, and the battleships would have to wait until fall of 1942 at Guadalcanal to serve as screens to carriers and even engages enemy battleships in gunnery duels.

We can then look to Midway to draw differences 6 months into the war. One is that the IJN operated all their carriers (here 4) as a single mass working together to maneuver and launch strikes. However it would be another year before the USN was experienced enough to do that, so here 3 carriers operated separately, all with their own screens of ships. YORKTOWN for instance as Task Force 17 had the carrier, 2 Heavy Cruisers, and 6 Destroyers. The Carrier would be int he middle, with the other ships a mile or so off in a great circle around her, and all ships would be free to maneuver as needed to avoid attack as we can see here: http://www.flightjournal.com/wp-content/uploads/2012/03/80G-701882-CV-5-Hit-by-Torpedo-14-45.jpg?40e310

As the war dragged on the USN grew in both skill and numbers so that by 1944 at Leyte, the Fast Carrier Force of the USN had immediately at hand 5 Large Carriers 5 Light Carriers, 6 Fast Battleships, 8 Cruisers, and 45 Destroyers. Within a larger fleet of over 300 warships.

Sources: War Plan Orange: The U.S. Strategy to Defeat Japan, 1897-1945 by Edward Miller

Pacific Crucible and Conquering Tide by Ian W. Toll

The First team by John Lundstrum

Neptune's Inferno by Hornfischer

Shattered Sword by Parshall and Tully