You can send SMS through Dingtone because you have a real US number provided by Dingtone. It has nothing to do with your device. Therefore, what you can do on your phone with Dingtone can be done on other devices.
If you have a Dingtone phone number then you can send and receive SMS, even on iPads, iPods and tablets. If you don’t have a Dingtone number then you can only send but cannot receive SMS. But that won’t take place in Dingtone because Dingtone gives you a US number by default as soon as you start your first call using Dingtone. It just happens that the default number Dingtone gives you will become invalid after some time while the purchased Dingtone number won’t go expired so fast.