Incognito in the Realm of AIs

When you open a new chat in your AI pal, you (I as well) probably don't pay close attention to the tiny icon on the top right of the page. It's a different icon in every AI, but the function is the same: Incognito or Temporary chat.

Now, from the get-go, even the name of the functionality isn't the same. So, which is it: incognito or temporary?

At first, 'temporary' seemed more of a clear term for me. I as a user understand it means the chat will be deleted after a short amount of time (though ChatGPT's definition of short time is 30 days, for some reason). Notice something is missing in the common understanding of 'temporary': Not getting saved in the history!

So, I prefer 'incognito', even though in the typical browswer jargon, the word indicates "Don't save anything". So, adding saving periods (Perplexity: 24h, Gemini: 72h, ChatGPT: 30d) makes little sense. Some call it "for security reasons", whatever that means.

Also, pay attention to the mention of training the model. From the four services I checked, only Perplexity is quiet about the issue of training with incognito chats. Although, I am not quite sure what use it has for ordinary users. If you choose a temporary chat, would it be so critical to prevent the AI from training with it?