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