I think the problem is that these terms had meanings before the last five or so years. There are setups that are actually accurately describable as "serverless"

I think the problem is that these terms had meanings before the last five or so years. There are setups that are actually accurately describable as "serverless" - for example, SQLite is called a "serverless database" because it's an embeddable library that just operates off a file as opposed to client-server DBs like Postgres or MySQL.