In my experience, German don't really make themed birthday cakes. That is why it's so difficult to find stuff here. They will bake a normal round shape cake, write on it...and decorate it with shop bought decor stuff. Icing is also way too sweet for them, so they decorate with cream most of the time.
An 'American' cake is the kind that is cut into shapes...or even baked in a shaped pan. I think she just called it that ,in order to clarify what she means. The Americans have set the stage for these kind of cakes. Another great website for alll your cake needs:
www.wilton.com
No supplier in Germany, now there's a business idea.