Around the turn of the 20th century, conventional battleship design emphasised the use of a range of gun calibres - 2-4 large calibre guns (typically between 9-12") for long range combat, and a battery of medium calibre (6-9") guns for the higher rate of fire at closer ranges. However, both gunnery testing and the operational experience learned from the Russian-Japanese War had begun to suggest that this paradigm was inefficient, as the bulk of damage was dealt by the largest guns, and the smaller calibre ones made fire control more difficult by increasing the number of shell impacts thus making it harder to determine which shell landed where. The logical conclusion was to switch the design of warship's main batteries over to entirely high calibre weapons, with only small calibre (3-5") secondary weapons to fend off torpedo boats. The Japanese were the first to attempt such a ship, but shortages of suitable weapons meant that the Satsuma had a mixed battery, leaving to opportunity for a truly revolutionary design of warship open to the British.
Yeah. Not a whole lot to argue with there: good stuff. I'm going to use this as a springboard to talk about a pet topic if you don't mind.

Mixed-armament construction (and, arguably, the emphasis on casemate weapons over turret weapons) was the legacy of the Battle of Lissa in 1866, the decisive Austrian naval victory over the Italian fleet. Admiral Wilhelm Tegetthoff's line-ahead tactics came to dominate theoretical conceptions of the battle line until the early twentieth century; when Russian admirals steamed at the IJN in line-ahead formation in the Yellow Sea and off Tsushima, they were practicing naval orthodoxy, and Tōgō's "crossing the T" maneuver was relatively novel (although he certainly wasn't the first to formulate it), as was his decision to open fire at what was at the time an extreme range. Also, the experience of the Russo-Japanese War helped induce the addition of another bit of tertiary armament to almost all dreadnoughts: torpedo tubes, which ended up being laughably irrelevant in battle in the Great War.
Anyway. The "all big gun" idea wasn't really the genesis of HMS
Dreadnought. The idea had been mooted before; the Italian navy had rejected such a proposal, but by 1904 the American, British, and Japanese fleets were already drawing up plans for all big gun capital ships for precisely that reason. (The Japanese ended up shelving the design for awhile due to material constraints and finished the
Satsuma predreadnoughts first, as you said.)
What really spawned the dreadnought was Fisher's interest in a global fleet and the means to project power over vast distances: centered around the battlecruiser, a new breed of fast hybrid capital ship with top-notch speed
and armament, which would sacrifice armor to obtain those superlatives. Fisher's focus was on battlecruisers; only budget fights with battleship enthusiasts, combined with Britain's changing strategic paradigm, forced the construction of HMS
Dreadnought as an interim compromise solution. With Russia increasingly neutralized, France friendly, and Japan allied, British planners in 1904-05 saw Germany as the new prime foe, and close-in engagements in the North Sea would dominate any potential war, not global campaigns by fast warships.
Dreadnought, under this reading, was an accident that derailed the original new naval paradigm. It came to define capital ships for decades in a way that was never actually intended.
The primary differentiation between dreadnought and battlecruiser was armor, not size, which is something that seems to be persistently surprising to many people who assume "battlecruiser" means "cruiser" means "smaller than a battleship". Battlecruisers were easily as large as any dreadnought (if not larger, in most cases); battlecruisers SMS
Derfflinger and HMS
Lion both displaced about 26,000 tons while their contemporary dreadnought class leaders SMS
König and HMS
Iron Duke displaced about 25,000 tons each. As with most classes of capital ship, "more armor" meant different things to different people. German battlecruisers tended to have about the same armor thickness in most areas as did British dreadnoughts, corresponding to a (generally) 100 mm-thickness advantage over British battlecruisers, and also enjoyed an improved bulkhead design that allowed German ships to take on considerably greater amounts of water while retaining buoyancy.
Only three countries built battlecruisers: Britain, at Fisher's behest (including two vessels raised by subscription from the dominions of Australia and New Zealand); Germany, to counter the British; and Japan, to ape the British. Japan's
Kongō class was essentially a superior version of the best prewar British battlecruisers, the
Lions; after the Washington Naval Treaty, they were extensively modified to exclusively burn oil (the original boilers burned coal sprayed with fuel oil) and incorporate more armor, and were eventually reclassified as 'fast battleships'. The German
Derfflingers were a slightly different paradigm, incorporating more armor than the Japanese and British designs, and were generally better suited to service in the North Sea theater while lacking the legs to conduct the long-range missions that the island nations' fleets regularly mounted. The three
Derfflingers made use of both coal- and oil-fired boilers instead of the hybrids employed by the Japanese.
Germany's battlecruisers played an outsize role compared to their relatively paltry numbers. SMS
Goeben, centerpiece of the
Mittelmeerdivision, eluded British and French pursuers at the outbreak of war to reach the Ottoman Empire, where her presence eventually contributed to the crisis that brought the Ottomans into the war. Turkey's entry fundamentally changed the conflict, and
Goeben effected it with spectacular efficiency. Renamed
Yavuz Sultan Selim, she became the flagship of the Ottoman fleet (still crewed primarily by Germans) and after the war she was the flagship of the Republic of Turkey until the 1970s.
Yavuz was the last battlecruiser in the world to be in service.
This is not to undersell the relevance of the battlecruisers that spent the war in the North Sea; they formed the vanguard of the
Hochseeflotte and enjoyed a favorable kill ratio over their British opponents.
Britain's battlecruisers had a decidedly more mixed career during the conflict. There were successes, to be sure. Their superior speed and armament outclassed the German light-cruiser raiders that dispersed into the world's oceans at the outbreak of war, and British battlecruisers confronted the German
Ostasiengeschwader off the Falklands in December 1914, crushing the only major German cruiser command outside Europe and ending any real threat to global commerce until the onset of submarine warfare. That extra speed came in handy: the battlecruisers were easily able to catch up with the fleeing Germans after the initial skirmish, and in a strategic sense their speed was crucial in allowing the battlecruisers to leave the Grand Fleet and return before the
Hochseeflotte could take advantage of their absence.
But more seriously, Britain's battlecruisers were not well protected enough for a stand-up fight. In the opening phase of the Battle of Jutland, the German battlecruisers of Franz von Hipper's I.
Aufklärungsgruppe sank three British battlecruisers for no loss of their own. (Later on in the battle, after the main fleets engaged, the battlecruiser SMS
Lützow sustained 24 shell hits from British dreadnoughts and was forced to withdraw under tow, but took on too much water and had to be abandoned and scuttled before she could make port.) All three - HMS
Invincible, HMS
Indefatigable, and HMS
Queen Mary - were destroyed by catastrophic explosions with few survivors. Several other battlecruisers, including HMS
Lion, sustained heavy damage. Vice Admiral David Beatty, the commander of the 1st Battlecruiser Squadron, reportedly commented that "there seems to be something wrong with our bloody ships today" after hearing that HMS
Princess Royal had been damaged (erroneously reported as destroyed). The engagement exposed severe defects in British capital ship construction, munitions safety, and munitions composition. These problems were only somewhat addressed during the war; fortunately for the British battlecruisers, they never had to do battle with the Germans again despite a few near misses.
British battlecruisers remained an integral part of the Royal Navy during the interwar years, with design somewhat improved in later models to account for the armoring issues that came up at Jutland. These efforts, while probably sufficient for First World War opponents, proved to be seriously flawed against Second World War ones. In 1941, the newest and most powerful battlecruiser, HMS
Hood, was engaged by the modern German battleship
Bismarck.
Hood had been launched in 1920, but underwent some modernization programs along with the HMS
Repulse and
Renown to keep abreast of naval technology. Those programs didn't seem to help much. During the battle against the
Bismarck,
Hood sustained hits on the aft turrets that apparently inflicted severe damage; shortly afterward, the ship was destroyed by an explosion in her aft magazine, although the exact cause of the explosion remains under some dispute. Later that year, HMS
Repulse - along with the modern battleship HMS
Prince of Wales - was sunk by Japanese torpedo bombers off Malaya.
Repulse hadn't received all the upgrades that
Renown and
Hood had gotten, but more importantly, she had no air cover and had to defend herself with her native AA emplacements, which were hopelessly inadequate to the task.
HMS
Renown was the only modernized British battlecruiser to survive the Second World War. After engaging the
Scharnhorst and
Gneisenau during the Nazi invasion of Norway, she mostly served in a secondary role, bombarding Axis coastal installations and providing fire support during Operation TORCH. She was sold for scrap in 1948.
HMS
Furious, a special battlecruiser constructed by Fisher as part of his (ludicrous) "Baltic Project", was converted to an aircraft carrier in construction. She was rebuilt with a better flight deck in the 1920s and continued to serve as an aircraft carrier throughout the Second World War. Like
Renown, she was scrapped in 1948.
Furious' two sister ships, HMS
Courageous and HMS
Glorious, also became aircraft carriers but were sunk in the early part of the Second World War.