One way that I look at it is that if you have a strong affinity to an element, your techniques will not only become more powerful, but you'll be able to create that element and manipulate it in more ways than one.

Kisame obviously has a strong Water affinity, and was able to create a tidal wave where there was no water present. Kakashi used water techniques against Zabuza, but he was simply manipulating the water by using the same jutsu Zabuza was.

He couldn't create mist/water himself, I don't think.

Look at the hokage battle! They were able to create earth walls, tidal waves, huge fire blasts...We still don't know enough about elemental jutsus to claim what is required for people to use them.

Someone like Sasuke, with fire as an element, can make fire from his throat (or stomach, or wherever it comes from). But i doubt he could manipulate wind the way Naruto is learning.