Unless the American carriers have managed to screw up one more technology (which is entirely possible) SMS is asynchronous. When you turn the device on it receives all the messages queued in the network.
If your device is off when your network gets an incoming SMS, the store-and-forward system just holds it until it can be delivered. This is exactly the same behaviour as Twitter or indeed e-mail.
My carrier can send SMS to multiple devices, or I can pick them up via a web portal, or via e-mail.
For SMS, though, the reader (often a mobile phone device) has to read the message the moment it arrives (or it, well, won't arrive). Since tweets are not limited to one person, reading Twitter can happen asynchronously.