And don't forget that both can be measured at either the crankshaft or at the wheel, which are often much different. So make sure to compare apples to apples, if that's what you're doing.

I grew up with BHP meaning British HorsePower, but I've often seen reference to it lately as standing for Brake HorsePower, apparently referring to the fact that the denotative way to measure it is to figure the amount of pressure applied to a friction brake required to stop the crankshaft. I don't think I've ever seen Base HorsePower.