Poe.com should explain what the terms they are using mean in their documentation. Once said that I don't know about the specifics of Poe.com, but I have seen that "ChatGPT" has been used as a generic name, like kleenex and google causing confusion and misunderstandings.
Even OpenAI used "ChatGPT" when they announced their Chat API. Due to server-side configuration, this API might not return the same response as the web and iOS OpenAI ChatGPT apps. AFAIK this configuration hasn't been disclosed to the developers using the OpenAI chat API can't assure that their implementation is delivering the same outcomes that can be obtained from the "original" apps.
As Andrew T.'s answers says, GPT comes from Generative Pre-Trained Transformation. The suffixes are used to identify the variations of the original implementation of a complex knowledge base. Including words like "Turbo" is likely that they have been introduced due to an "entrepreneurial" motivation, probably induced by a fundraising, competitive, business mindset.
Regarding Google "summaries", be careful as you might wrongly attribute the content. Google employees have been careful to include details of the source of the "summaries" that the search engine returns. The search engine is fast at presenting results; Google doesn't warrant correct results. As Google also has its own "ChatGPT", due to the "ChatGPT hype", their search engine might, as ChatGPT does, hallucinate and return plausible but incorrect content.
On July 25th, 2023, I created an account at Poe.com. The documentation is very scarce; even Poe (Software), the Wikipedia article about this application software, has messages mentioning that the article requires improvement.
Poe.com is a software application that allows users to create and share bots. That might be why you see the same user interface for all bots; Poe.com might avoid the burn of having to create the UI for bot creators. Probably this might be seen as a low-code platform specialized in creating bots.
It includes bots operated by themselves; one of them is named ChatGPT.
Please be aware that despite being called ChatGPT, it's not the same as https://chat.openai.com. The "Learn more" link at the bottom points to the Poe.com about page, https://poe.com/about. It's unclear; because of this, it might be better to look at https://platform.openai.com/docs/models/overview. From this page:
The OpenAI API is powered by a diverse set of models with different capabilities and price points. You can also make limited customizations to our original base models for your specific use case with fine-tuning.
|A set of models that improve on GPT-3.5 and can understand as well as generate natural language or code
|A set of models that improve on GPT-3 and can understand as well as generate natural language or code
|A model that can generate and edit images given a natural language prompt
|A model that can convert audio into text
|A set of models that can convert text into a numerical form
|A fine-tuned model that can detect whether text may be sensitive or unsafe
|A set of models that can understand and generate natural language
|A full list of models that have been deprecated
What customizations might have the Poe.com bot named "ChatGPT" is unclear.
You should look at the details of each bot to learn who operates / created it and if there is information about what the bot name means. You might also have to look for reliable sources about Artificial intelligence, in this case, more sources specialized in Large Language Models (LLM), Generative Pre-Trained Transformations and OpenAI-produced content.