These two phrases are used generally to refer to the same thing: a text rather than a voice message. Here's one definition of text messaging:
"Sending short text messages to a device such as a cellular phone, PDA .
Text messaging is used for messages that are no longer than a few hundred characters. The term is usually applied to messaging that takes place between two or more mobile devices."
But "SMS" means Short Message Service, which is a SERVICE for sending SHORT TEXT messages to mobile phones. So you can see that the generic name for the message is "text message", while"short message" came into use(esp.thoroughout Asia) from the same fo the service. In the U.S., for example, only"text message" is used. Perhaps this is due to the name used by marketing folks in their sales pitches?
It thus seems that the most correct technical or generic term for this kind of message is "text message" and that "short message" is a result of a marketing campaign's name for this kind of communication. Remember those things called"beepers"(or "pager")? Some of them could also deliver short text messages.
It seems to me the more logical term is "text message" because the most important part of this kind of message is that it is "text only" and does not have voice; it could also be fairly lengthy (i.e., not just a very short message). On the other hand, a "short message" is first of all short, i.e., not very long, but it could be either text or voice.
But I guess the bottom line is: use whichever term is appropriate for the region in which you live or use it. But if you work in IT, you would probably use the more standard technical term" text message".
