Some people don't think you should call the iPhone a smartphone, as it's not an open platform, while most people seem to agree that phones running SymbianOS are indeed smartphones. Well, at last the S60 and UIQ ones. The accepted distinction between open and non-open platforms seems to be that open platforms let you install third party native code. However, seeing as most open systems are more or less closed, as they only give third party developers access to a select subset of the system's API:s, it might be more useful to think of open vs. closed systems as a scale that ranges from completely closed to completely open.
A PC running an open source OS (or the Neo 1973 smartphone) is about as open a platform as you'll find, while a wristwatch is a completely closed system. Between these you have systems like the iPhone, that lets you install widgets, with little access to system functions, feature phones that let you install Java midlets and typical smartphones, that let you install native code apps, but don't give you access to the full set of system API:s, and won't let you replace system components.
The iPhone is less open than a typical feature phone, but it's also more "smart" than those, as it's running a real OS, just like smartphones. This just shows that categories like feature phones and smartphones are too simplistic. It was a good idea to use these categories 5 years ago, when open phones was something new and exciting.