That's true. British English and American English (and Australian english for that mater) are pretty much the same except for the accent differences. There is no dialect difference between them (like with the Mandarin and Cantonese Chinese language.)

But our colloquialisms and some things are different.

America we say "vacation." England they say "holiday."
We say "truck." They say "lorie."
We say "Semi-truck." They say "reticulated lorie."
We say "french fries." They say "chips."
We say "soccer." They say "football."
We say "baby stroller." They say "pramulator."
We say "gas station." They say "petrol station."
We say "piece of paper." They say "piece of parchment."