Private browsing may on the surface seem secretive and similar to anonymous surfing, but in reality, this special setting is mostly to hide your activities from others using the same computer.
Your online activities are in no way disguised for those beyond the computer, explains Firefox developer Mozilla. Websites and online services can still collect information about the pages that you visited while in private mode, even if you are not logged in.
In addition, your IP address can still be seen, and your Internet provider or the administrator of an external network – your employer, for example, has access to pages you visited on their connection.
In Firefox, private browsing means that passwords, user history and cookies aren't saved, and downloads aren't shown in Firefox's download manager. However, they're still saved in the computer, as are bookmarks that are saved while you're in private mode.
Even browser providers can observe users in private mode. If you use Google Chrome's Incognito mode, the Google search will still make search suggestions in the browser based on your location or activity.
For Chrome, Incognito mode means your browser history and information entered into forms won't be saved. Cookies and site data will still be saved, but then deleted when the private session is ended. – dpa