"just what is the logic behind the US/French way of assigning values to these words???"
I don't know that there is a logic. I first learned that there was a difference in high school, though I did not know which one had prior usage. Could be that we just plagiarized the French usage. I can guess that they figure that it was just logical to say that after a billion should come a trillion, quadrillion, and so on.


"- in modern 'international' English, do these words have one standard accepted definition? Are they in fact used?"
I heard them used a few times in high school and maybe middle school. For those of us who actually use numbers that big - and I have used numbers of that size and vastly larger for real problems - with a few exceptions, it is more common to use scientific notation, keeping only a few digits of precision. For example to express the constant known as the permittivity of free space, we would write 8.852 e-12, pronounced either as "eight point eight five two EE minus twelve" or as "eight point eight five two times ten to the minus twelve." The speed of light in a vacuum would be 3e8 m/s, or "three EE eight meters per second."

"- (insert desperately-justifying-own-lack-of-knowledge-and-hence-not-using-them-in-proof emoticon here ) given obscurity/dual definitions, do they really qualify as 'officially recognised'?"
I never thought about it.

"- how bizarrely different the wording is of entries in the same dictionary for such closely related words!"

indeed!

k