It's because of Session and Cookies.
*en.wikipedia.org/wiki/Session_(computer_science)
*www.allaboutcookies.org/cookies/
Each tab is referred to as each session, and that's the reason they are not mingled up with each other.
On the other hand, try to login in Gmail and once you logged in, try opening Gmail in another tab of same browser. You'll be automatically logged in.
But if you are logged in to Gmail using Chrome and you try to open Gmail in some other browser (Like Firefox, Opera, IE) you won't be logged in automatically.
So it's all due to sessions and cookies.
Though cookies doesn't have much role to play,