After playing with the APIs, it seems there's something annoying happening with the terminology right now. "ChatGPT" and "davinci-003" aren't equivalent, but it isn't entirely clear how.
The biggest difference is that ChatGPT can remember earlier parts of our "conversation", davinci can't. I suspect that this is just the result of the interface, that it is being presented with our conversation history has an input. However, I haven't found anywhere that actually makes it clear how this aspect works. Can anybody shed some light?