The S is there simply to differentiate it from a technical standpoint. It rolls off the tongue a lot easier than "iPhone 3G second edition" or "iPhone 3G mid-2009 release." You can't call it a "third generation iPhone" because that confuses the fact that the "Second Generation" iPhone runs on a Third Generation cellular wireless network. And you can't call it the iPhone 4G, because it's neither the 4th Generation iPhone, nor does it use a 4G network.
Besides, most conversations are going to go something like "Oh, an iPhone! Is it the new one?"
You don't emphasize in common speech that it's an S model. It's just a iPhone. Yeah, the new one.
I don't even call my iPhone 3G an "iPhone 3G" in common speech. It's just an iPhone. The current model. In a week it'll be "last year's" version.