No, a private browsing window only stops local browser history being kept. A signed in account still saves the conversation on the server regardless, and Docognito changes neither part of that, since it works on the page rather than on the browser or the account. It behaves the same way inside a private window as outside one.
Two different layers, easy to mix up
A private browsing window, whether Chrome calls it Incognito or another browser calls it something else, operates at the browser level. It stops that browser writing new entries to your browser history, and it discards cookies and site data once every private window is closed. That is a real and useful privacy feature, and it does exactly what it says.
An assistant's saved conversation history operates at a different layer entirely, tied to your account rather than to the browser. Signing into ChatGPT or Claude inside a private window still signs you into the same account you would use anywhere else, and the conversation itself, which OpenAI and Anthropic still receive and store still applies. The private window changes nothing about what your account saves once you are signed in and sending messages.
What each layer actually controls
| What people assume | What actually happens |
|---|---|
| A private window keeps the conversation off the record | It keeps the visit out of local browser history, the conversation itself still saves to the signed in account |
| Closing the private window ends the conversation | The conversation stays in your account history until you delete it there, closing the window has no effect on that |
| Incognito and Temporary Chat do the same job | Incognito is a browser feature, Temporary Chat and Incognito chat are account features built by each assistant for this specific purpose |
| Signing in inside a private window is somehow different | It is the same account, the same login, and the same saving behaviour as signing in anywhere else |
The second row is the one that catches people out most often, since it feels intuitive that closing the window should close the conversation with it. It does not, because the conversation was never stored in the window.
What closing the browser or restarting the computer changes
Neither action reaches the account layer either. Quitting Chrome entirely, or restarting the computer, ends the private browsing session and wipes whatever that session was holding locally, but it has no way to reach back to a server and undo a message that already saved there. If a conversation was sent while signed in, it exists on the account the moment it was sent, independent of how long the browser stayed open afterward or what happened to the device once you were done.
The feature actually built for this
Both assistants ship a dedicated mode for exactly this situation, and it is worth using directly rather than relying on private browsing to do a job it was never built for.
On ChatGPT, use Temporary Chat
Start a new conversation using Temporary Chat, found in the new chat menu. Messages sent in that mode are not added to your saved chat history.
On Claude, use Incognito chat
Start a conversation with Incognito chat, found in the same place you would start a normal new chat. It keeps that conversation out of your saved history the same way.
Reach for one of these when the goal is keeping a specific conversation out of your account history. Reach for private browsing separately, when the goal is keeping the visit itself out of your local browser record. Using both together for the same conversation is fine too, and covers slightly more ground than either alone, since one addresses the account and the other addresses the device.
Where Docognito actually sits in this picture
Docognito changes the page, not what is saved anywhere
Even with Docognito running, nothing changes about the address bar, which still reads claude.ai or chatgpt.com, whether the window is private or a normal one. The extension also has no effect on what your account saves, since that decision belongs to Temporary Chat or Incognito chat, not to a browser extension. Docognito only redraws what the tab looks like while it is open.
This is the reason the two tools pair well rather than compete. Private browsing, or the assistant's own Temporary or Incognito mode, controls what gets recorded. Docognito controls what a person glancing at your screen actually sees while you work, and it does that job identically whether the window is private or not.
History and appearance call for different tools
For keeping the conversation itself out of your saved history, use Temporary Chat on ChatGPT or Incognito chat on Claude, since a private browser window was never built to reach that layer. If you want the page on your screen to stop announcing which assistant you are using, Docognito does that in any window, private or not. Use the tool built for the layer you are actually worried about.