> but that term [battleships] is sometimes used colloquially to refer to any surface warship other than carriers

Really? I wouldn't be surprised to hear someone call a frigate a cruiser or a littoral combat ship a destroyer or an amphibious assault ship a carrier but everyone knows battleships are the biggest big-gun ships out there.

I think so, at least for some people who don't have an interest in military stuff or machines generally. Similar to the way any armored but unarmed truck may sometimes be called "a tank." (https://duckduckgo.com/?t=ffab&q=police+tank&iax=images&ia=i...)

I try not to judge, I'm probably equally wrong without knowing it about things as far outside my area of interest.

I would not be surprised if many people who don't have knowledge of naval vessels would use "battleship" as a generic term for "surface naval vessel". A possible driver of this could be the "Battleship" game.

I would also not be surprised if there were many people who'd never heard the terms "destroyer" or "cruiser".

But the "Battleship" game has five different kinds of ships, only one of which it calls a battleship, and it does include cruisers and destroyers.

“Warship” would be the correct colloquialism, I think - battleships were specifically characterised by heavy armour and large caliber guns.

Does the USA even have a battleship?

I thought they were obsolete.

They're obsolete. There was some debate in the 90s and 00s over whether they should be kept around since they had an incredible amount of firepower and some people still thought that maybe contested beach landings were a good idea. But ultimately they were stricken from the Navy and are now museum ships.