And they don't get spam filtered, nor do I get phishing Tweets from people pretending to be my hosting company.
Remember all those harebrained schemes to charge companies tiny amounts of money for guaranteed-delivery emails with verified sender IDs? Twitter just deployed that system right under our noses.
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.
...yet.