[ska]

It's not as simple as company size, it's responsibility and authority.

Necessarily the nature of the job changes a bit if you are a the head of an organizational unit of 600, or 60, or 6. But it changes fundamentally if you have ultimate budget authority, hiring/firing, etc.

Agree there are a lot of somewhat ridiculous titles in early stage startups (ever seen a 5 person company with 3 "C" levels?) but even when you are small (but growing) there is a role distinction between exec and non-exec roles, and there is a difference worth drawing between director-in-name and director-in-fact positions.

If you are truly acting as a director of engineering, I'd expect you have broad authority to act; you don't ultimately decide your budget or technical goals (but you should be involved in determining both) but within those constraints you have most of the decision making responsibility for how & who.