Could it be incognito browsing? Or you just use an alternative browser, eg I use Chrome normally but Safari when trying to view Apple WWDC videos.
Or, instead of two different browsers, you can use xraru [1] to ad-hoc launch as many independent ephemeral "incognito" sessions with the same browser as you like. This way, next to enhanced privacy, you also get as a bonus some protection from malicious websites stealing your cookies/local files/etc...