Keep in mind that the information in the link you provided only applies to the developer models, which are only accessible via API and OpenAI Playground.
OpenAI's developer relations person confirmed it a little whiles back:
> [..] I made the comment elsewhere, but the models are always changing in ChatGPT.
From the OAI API, gpt-4 seems to be an alias for the most recent model two weeks after it is released. There has not been a release since 0613.
https://platform.openai.com/docs/models/gpt-4
e: from your edit,
"Note the context size is 4095. Their model has been heavily optimized for speed and, presumably, cost."
No, they are restricting context size to make inference on the chat interface cheaper but that does not mean it is a different model.