Every time this topic comes up, I mention this... so why break with tradition?
Historically, dreadnoughts are (rather primitive) battleships... When/how did the idea that a "dreadnought" is a "large battleship" come from?
That's not really correct. Here's the actual history of the terminology, w.r.t wet navies:
The term "battleship" derives from "line of battle ship", an alternate term for "ship of the line". "Battleship" superseded "Ship of the Line" in the late 19th c.; basically, as steel capital ships began to become standardized. So, "Battleship" as a naval ship classification predates "Dreadnought".
In 1906 the British introduced the first of a new type of battleship, being much larger than her predecessors and carrying a uniform armament of large guns (preceding designs had generally carried three or four different sizes of weapon). This was HMS Dreadnought (the name was just the next in the ongoing British battleship name progression; it was a traditional Royal Navy name and an HMS Dreadnought had fought at Trafalgar), and all all-big-gun battleships became known in the English language as "Dreadnoughts" or "Dreadnought Battleships". So, dreadnoughts were a large and powerful sub-type of battleship. Following this pattern, "Super Dreadnoughts" were the next big leap in battleship size (HMS Orion, ~1910) and were a sub-type of both battleships and dreadnoughts.
By the Second World War, virtually all of the old pre-dreadnoughts were out of service and the term "dreadnought" was now far less useful in distinguishing battleship types and became less common, although Bismarck, Yamato, etc, were all still dreadnoughts in any sense of the term.
How all that translates to a Sci-Fi setting is of course going to vary, but that's the history of the terminology.