This has annoyed the crap out of me for a long while too. I never found out how to drive the difference -- "that's not git, that's GitHub!" -- home to people who'd just answer "What are you on about, it's the same thing!" before this idea struck me right now:

"No, they're different things. Just like GMail is one e-mail server (and client), but GMail isn't the same thing as e-mail."

Gonna try that next time I get onto the subject.