Headscale is server only. Netbird is the whole stack (basically does the same thing but completely different software/implementation)

But the tailscale client is open source too

Doesn't that also then make tailscale completely open source?

No their "real" backend is proprietary. Headscale is a separate implementation that they also maintain. It's intended for self-hosting your individual Tailnet. I'm assuming if you tried to use it as a corporate VPN you would run into limitations.

Their clients for proprietary OSs are at least partly proprietary too.

To be honest I find this all a very reasonable set of compromises. It means I'm comfortable using their proprietary service without feeling like I'm getting locked into a completely closed ecosystem.

What? The original coordination server, which is not running headscale, is closed source so yes, they are still a closed source company

Not on Windows and iOS. And on the mac, the most useable client isn’t open source either.