A better name for a push-pull output stage would be a 'see-saw' configuration. However it grates to those who use the 'old terms' 'correctly'. It's how language develops, it might even catch on.
I'm sympathetic to the mistake, I might even have used words like that when explaining the how and why of a totem pole output to somebody. It's likely the person has heard the term push-pull, and their first exposure to a circuit that had a 'drive in both directions' sort of behaviour was a totem pole. They are totally different circuit used in totally different situations.
I can understand why somebody might describe a totem pole output stage as a push-pull, but most people call it a totem pole. The configuration you've shown is the prototypical 'push-pull' arrangement.
