I don't own an S3, so cannot comment on the options for saving pictures - the phone will be using Samsung's version of the message app, which I've never used. I agree that there ought to be an option somewhere, but don't know what it is. My first guess would be to long-press the image and see what options pop up (my HTC's message app has "save" as the first option).
If you can't find an option in the app anywhere, and nobody else suggests anything, try installing an alternative messaging app from the Play Store (Handcent, Chomp, etc) and see whether that app lets you save the pictures.
However, your original question is a bit puzzling: the standard for sending pictures in messages is MMS. I'm not sure what you were expecting it to be sent as, but on any phone, android or otherwise, that's what I'd expect to be the default. There are proprietary alternatives, which depend on both parties using a specific app (e.g. Whatsapp) or a specific operating system (e.g. iMessage), but the platform-independent cross-network standard is MMS. If you wanted to send it as something else (e.g. an email attachment) then you should use a different app.
