If you want to open two different accounts in the same site (like Facebook, Gmail etc.) simultaneously using Firefox try the following method –
1. Log into the first Facebook account in Firefox
2. Press Ctrl+Shift+P to open a New Private Window.
Alternatively you can click the File menu on top left and choose “New Private Window” from there.
Voila! You will be allowed to login to a new Facebook account from the private browsing tab.
To do the same from Chrome check out this post.