In what way are you required to read an SMS the moment that it arrives?
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.
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.