Officially anise, star anise, and fennel are different plants. However, I have heard them used to refer to different parts of the same plant here in the US. If you get the seeds though, it is exactly the same as far as I know. You can actually use all parts of the plant in cooking and I have seen in some shops where they call the leaves anise and the bulb itself fennel. They had a whole iron chef america show devoted to fennel recently.

anise - http://www.uni-graz.at/~katzer/engl/Pimp_ani.html
fennel - http://www.uni-graz.at/~katzer/engl/Foen_vul.html