I'm confused. I think that in German,

eine Milliarde = 1,000,000,000 (billion in English)
and
eine Billion = 1,000,000,000 (trillion in English)

Apparently billion (Eng.) is not the same as Billion (Ger.). Is that right?

In English the names are:
million - 6 zeros
billion - 9 zeros
trillion - 12 zeros
quadrillion - 15 zeros
quintillion - 18 zeros

What are the corresponding words in German?

Thanks.