So if I understand what you're saying, if someone asks you "Hey, could you recommend me a general purpose Linux distribution?", you'd recommend them Ubuntu Server rather than just straight up Ubuntu?

I'd agree both could be used in a general-purpose way, but I'd definitively call one of them more general-purpose than the other.

Most Linux server distributions would be expected to be headless.

"General purpose" Linux distributions (not "server") typically would include a GUI desktop.