just what is the logic behind the US/French way of assigning values to these words???

I was taught that the US way is to increase the name by one rank for every three zeros and the British way is for every six zeros. Thus
1,000             is  one thousand US  vs  one thousand British
1,000,000         is  one million      vs  one million
1,000,000,000     is  one billion      vs  one thousand million
                                          (or "one milliard")
1,000,000,000,000 is  one trillion     vs  one billion
                                          (or "one million million")
10E15             is  one quadrillion  vs  one thousand billion
10E18             is  one quintillion  vs  one trillion
10E21             is  one sextillion   vs  one thousand trillion
10E24             is  one septillion   vs  one quadrillion
etc.

Does this sound familiar to anyone?