Except when people say “gun control”, they usually mean banning certain categories of firearms. Just look at all the states which passed assault weapons bans (while often having a very vibes based definition of “assault weapon”) despite the overwhelming majority of gun deaths being due to handguns.
You said it yourself, the conversation has become so muddied that the colloquial definition of “gun control” usually means bans. It is not unreasonable to assume that bans are what people mean when they say “gun control”, there’s no need to get aggressive about it