Isn't this the entrepreneur-or-freelancer divide? Is the thing you're working on making you money while you sleep (entrepreneur, "startup" is appropriate) or do you only get paid when you work (freelancer, "self-employed" is appropriate).
Not saying this distinction is useful, but at least it's a common way of talking about the various forms of "being your own boss".
Not saying this distinction is useful, but at least it's a common way of talking about the various forms of "being your own boss".