I know what you're getting at, and there does tend to be a difference between corporate CTOs of non-technical companies, start-up CTOs and CTOs of large tech companies. However, they're all very much real (but different) roles. You can't just throw any developer into a CTO role and expect it to work. Certainly developers do move into CTO roles (myself included) but there's a lot to learn/do beyond writing code.
No, calling yourself "CTO" of a 2 person company does not make you a CTO. You might be a manager, a founder, or some other title, but you're absolutely and unquestionably not a CTO.
That's like saying you start a company by yourself and you can't call yourself a CEO. CTO, at any size, still has a lot of concerns that aren't just code level, so the title is valid.
However, context is very important. Anyone that looks at someone's resume and sees that they're the CEO of a single person company will understand that they're on a different level than the CEO of a publicly traded company.
EDIT: the other thing that gets conflated here in these title discussions is non-technical founders thinking they need a CTO, when really they just need a lead developer. That definitely muddies up the conversations.
That said, I think that a CTO of a 2 person company and a 500 person company deal with a few of the same issues, but a lot of the same responsibility (tech leadership, the final arbiter of tech decisions).
In my case, I'm not even a founder of the company of which I'm CTO, actually I'm not even a director. I was appointed CTO by the board, of which I'm not a member, and the company is profitable.
