Yup, these are just terms, to me. Call it a banana if you want. I like the term "battle cruiser", like in Star Trek. It sounds, cool.
I don't see a good reason to argue over such terms.
I somehow missed this the other day. I tend to agree with you on the futility of arguing about the terms but I can point you to some historical forums where you can read literally hundreds of posts arguing over what exactly is and is not a Battleship, Battlecruiser, or a "Large Cruiser".
For the uninitiated, the Battlecruiser concept was born at a time when Battleships were large well armed and well armored ships but FAR too slow to actually force enemy cruisers into battle. At the time Battleships typically could only obtain around 20-23 knots while typical cruisers were around 10 kn faster.
Historically Battleships were usually built to what was called the "Balanced Battleship" concept. That simply means that they were sufficiently armored to resist their own shells.
Side note, All-or-Nothing Armor:
Originally Battleships were armored from bow to stern. However, as guns got larger and more powerful it became impossible to build a ship armored from bow to stern against heavy guns that could also carry heavy guns and still be able to float and move. To solve this riddle, Naval designers came up with the all-or-nothing armor scheme. This meant that instead of providing armor for the entire ship, only the critical parts of the ship (magazines, engineering spaces, and enough buoyancy to keep the ship afloat) were armored. The rest of the ship had virtually no armor at all. This is why, for example, Wisconsin collapsed her entire bow in the 1950's. There wasn't any armor up there.
Back to the ships. Battlecruisers were conceived largely to be able to take out enemy cruisers. Battleships were more-or-less incapable of this since cruisers were so much faster so they could simply run away. The general concept of a Battlecruiser was a ship with the armament of a Battleship and the speed of a Cruiser. The idea was that it could destroy anything it couldn't outrun and outrun anything it couldn't destroy. In order to accomplish this, armor was sacrificed.
The only class of ships ever officially authorized for the USN as a Battlecruiser was the Lexington Class authorized in 1916. Six ships were laid down but none were finished as Battlecruisers. When the Washington Naval Treaty came into force the USN scrapped four without completing them and converted the other two into the Lexington Class Aircraft Carriers Lexington and Saratoga. Lexington was sunk at Coral Sea, Saratoga survived the war and was sunk in the atomic tests at Bikini.
As Battlecruisers the Lexington's would have had eight 16" guns and a 5-7" armor belt. Compare that to twelve 16" guns and a 8-13.5" armor belt for contemporary USN Battleship designs. What the Lexington's would have gotten for the reduced armor is a LOT more speed. Contemporary USN Battleships had a top speed of 23 kn while the Lexington Class Battlecruisers would have been able to attain 33+ kn.
At the Battle of Jutland both the Germans and the British used their Battlecruisers as effectively "fast battleships". They wanted to use them because they had big guns like the Battleships but several of them exploded in the battle because they were not armored sufficiently to take on their own size shells. This wasn't a design failure so much as a misuse. The Battlecruisers had not been designed to stand in a line and slug it out with equivalently armed ships. The designed intention was for them to run away from anything with equivalent guns. In wartime practice the Admirals wanted as many big guns as they could get so all the big gun ships had to stand and slug it out even though the Battlecruisers were known to be incapable of actually doing this.
Thus began the process of creating a "Fast Battleship". The Iowa's (built ~20 years later) had armor comparable to the old USN Battleships AND speed comparable to the never-completed Lexington Class Battlecruisers.