Well, over time, definitions mutated a lot....
From WWI to WWII, this generally summarizes some of your list:
Battleship: Guns 11" or larger, (normally 8-12 of said guns) typically, 25,000 tons or more, heavy armor. WWI ships had top speeds about 18-20 kts. WWII-designed battleships were about 28 kts or more.
"Dreadnought" essentially = battleship. However, usage of the term died out after WWI. Prior to the launching of HMS Dreadnought in (1906 I believe?) Battleships had, typically, 4x11" or 4x12"guns, and a mixed assortment of medium and smaller guns, and were painfully slow. The Dreadnought was a radical break, and after that Battleships had 8 or more 11-12" guns, dispensed with the mish-mash of medium guns, and were much faster. Ships similar to Dreadnought were called "Dreadnought-Battleships" to differentiate them from the old pre-1906 Battleships. After WWI, all the old "pre-dreadnoughts" were gone and it really wasn't necessary to use the Dreadnought term.
Battlecruiser: Same as a Battleship, (often they were even larger) but very light armor, and much faster speed. But shown to be too fragile in WWI. In WWI, the battlecruisers had the 25-30 kt. speed. By WWII, new battleships had heavy armor and were just as fast as the WWI battlecruisers rendering the battlecruisers obsolete.
BCs had an unfortunate tendency to blow up the first time they took hits. After WWI I believe only one was built (Hood) and all the rest under construction were either scrapped or turned into Carriers (Kaga, Lexington, etc.)
Heavy Cruiser: 8 inch guns, 10,000-15,000 tons. Light armor. May or may not have torpedoes depending on the country.
Light Cruiser: 6 inch or smaller guns, 7,000-15,000 tons. Light Armor. May or may not have torpedoes depending on the country.
Destroyer: Smaller than 6 inch guns, size varies wildly, essentially no armor at all. All had torpedoes of some kind.
Once you start getting into Destroyer Escorts, Corvettes, Frigates, things get awfully confusing and messy. All were ships usually used for convoy escort, and generally were smaller, much slower versions of Destroyers.
Of course, there are some odd exceptions, like the German "pocket battleships" (the size of a heavy cruiser, but some armor, and 4 x 11" guns), the USS Alaska and Guam, etc. that are hard to categorize.
Despite what you hear in the radio channels, AH has nothing bigger than a Heavy Cruiser. That's not a "battleship." It's an American heavy cruiser, 8" guns, no torpedoes (Americans didn't put torps on their cruisers.
