In my head, a startup is something that can scale, and possibly needs scale. So me selling woodworking will always be limited by how much I can produce, thats still a businesses but not a startup. Selling a SaaS product however makes little money in the start, but can scale sales virtually infinitely.
I think people have their own axis they divide this on. So none of us are correct. For some it's also a vanity thing, where entrepreneur or startup sounds better.