You got it. Mostly.
The bubble is the PM function. And it just keeps all the info 'in house'. So no emails are actually sent, it's just data traveling back and forth between the databases. And the 'Messages' tab is where all your PM's will show up.
It is private, so no one else can view them.
The 'Email' button is just that. It will send a email to that persons address using your address. This feature I am not really sure about, since if I wanted to send an email I would do it through my email account. But different strokes for different folks.