I think it's one of those cases where "you know it when you see it"
At first, the iPhone was more like a "feature phone", like the Instinct. It had some neat built-in apps, but the user couldn't add more of them.
Once it got an SDK, a place to get apps, and there was more than one model using the apps (e.g. iPhone 2G, iPhone 3G and iPod touch), then it magically became a "smartphone".
Perhaps it would be "smarter" if the user had more control, as with themes and what apps they want to add, but so it goes.
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A more recent question is, who's it a smartphone for?
I used to say it was the "smartphone for people who didn't know they needed one".
Now I hear people calling it "the smartphone for dumb people". (Because Apple won't let it have advanced options that might be too "difficult" for casual users). Which seems a bit too rude.