[oldtownroad]

Twitter is not a tech company: their commercial output is not technology, technology is just a tool, Twitter is a social platform. Musk is not acting as a CTO, a CTO doesn’t set product direction. A CTO delivers for other stakeholders using technology. Every company uses technology now, it’s not a differentiator. Even if a company is a technology company, the CTO role doesn’t change, a technology company still has a CEO. The CFO at a finance company doesn’t set product direction.

[danpalmer]

I see what you mean, but I don't think this is how it always works in practice. In these jobs the lines are often blurred. Some companies don't have all of them, and, say, the COO might do what would be a CFO role in another company. In a strongly tech-focused product (like a PaaS or something), the CTO could be effectively doing a CPO role. In many places the CTO may be the CISO as well. In a company that depends significantly on "financial engineering" the CFO might have quite a deep say in the product direction.

You're right that Musk is not a textbook CTO, but I think he has been quoted as saying he's also CPO, and that fits a lot better.