SAE is a formula to correct measured horsepower for differences in air temperature, pressure and humidity. RWHP is measuring power at the rear wheels, as opposed to Brake horsepower, which is at the flywhee. SAE correction is normally applied to both of them. With a manual trans, RWHP is usually about 15% less than BHP because of drivetrain losses.
Some people also use STD correction, which usually gives #'s about 2% higher, but is not as clearly defined (different people use different STD formulae). SAE is the standard correction in the US, used by all manufacturers.
I always thought that STD was the standard readings and could be higher or lower depending on the temperature .. etc. SAE will correct it to a standard so that in theory you would be able to compare readings since it is all corrected to that standard.
STD is a correction to what is called ACTUAL reading, which is what the dyno measures. It is just a formula, like the SAE formula, but standardized to a cooler, denser condition that gives a higher #.
There are many kinds of chassis dynos, which measure power at the wheels. Mustang and Dynojet are the most common. They give different readings because the Mustang dyno applies a load to simulate weight, rolling resistance and air resistance to simulate real world operation. Most Dynojets only have the resistance of spinning the drum. It's pretty complicated, but you usually measure lower with a Mustang, but some people say it's better for doing real world tuning (setting timing and A/F). Dynojets are more common and correlate well with flywheel or brake horsepower.