I would have to agree, I’ve seen headless referred to in both ways. The most common that I’ve seen is what you’re referring to now. Where a server or computer has no keyboard, mouse, and monitor and is primarily controlled over the internet with something like ssh.
Both ways can be seen as “correct” though. Just depends on how you view a “headless” system.
Seconded on this one. I use Yattee with Piped as my frontend, with an account as well, and it’s been pretty solid so far.