Liferay login isn't by site, it is to the server. Whatever you think you're doing, you're actually not.
Now you might say that if the user logs in on Site X that we want to do one thing when they log in but something else when they log in on site Y, but in either case it is still one login.
That said, login pre and post event handlers can check what the current source and choose whether to do something or not. They have access to the request header which means you can get anything you need to determine whether to do something or not.
Either way though, it is still a single login. If you're doing something like "in X add role ABC to user at login" and "in Y set a cookie for Z", you should be doing both of these when I log in because you have no idea if I know how to switch between the sites manually. They are, after all, just address bar changes away from each other. If you don't properly construct the environment for me regardless of the site I'm currently on, users may encounter unexpected results.
