Huh, TOTP and HOTP are pretty technical terms, and I generally don't hear them in places meant for general consumers to read (e.g. even Google Authenticator, which does TOTP and HOTP, doesn't say TOTP or HOTP). The general term, OTP is much more common, and is accurate for SMS.

Soooo, now you're arguing with me about what the person on the phone said? Where does that take the conversation?

I'm not trying to argue. I'm just saying that it's strange.