I definitely don't consider the Kindle to be a tablet, and neither do most other people. In fact, a lot of people own both a Kindle plus a tablet computer (iPad or Android-based tablet).
The Kindle is successful because it does one thing very well, and that's ebook reading. It essentially sucks at everything else. I love my Kindle for reading, despite the fact that it has an appallingly bad and klunky user interface.
The iPad is a completely different beast to the Kindle. And that's why both Amazon and Apple can be successful in the arena. Pundits like to claim they're competing against each other, but they're not -- at the moment. Who knows what the future will bring...