Well, it gets a LOT more complex than that...
BHP is the standard UK measure of horsepower. In the U.S., you have SAE Net and SAE Certified, which are slightly different tests and give slightly different results from BHP. Then you have PS - Japan and Germany use this rough Metric equivalent for HP, and most of Europe uses the same measure with a different name. The Australians, Chinese, and much of the Pacific Rim use Kilowatts, the actual Metric Power rating, which makes it hard to compare directly many of those cars to the Horsepower or PS used in much of the world...and if you talk pre '70s American cars, you get into the SAE Gross test, which resulted in inflated ratings of more than 40HP in some cases. All of these are measured at the crank.
Then we have WHP, or "true" HP, which is typically found by a rolling road. This is actually what's being transmitted to your tires in a gear that results in a ratio very close to 1:1, typically fourth. This is usually about 15%-25% less than the rating at the crank.
Finally, there's "Fiscal" horsepower, or CV, which isn't really a measure of power at all, but is a rating applied for taxing purposes in France and Italy.