Most people who say I put down XXX whp are talking about a dynojet number.
The main difference is as that shop claims, a mustang dyno can (generally) more effectively load the car than a dynojet can.
A mustang dyno, functions by calculating the weight of a drum (around 2560 lbs) with other factors. Those factors typically include the weight of the car and it's horsepower used to achieve a certain speed. The certain speed is used to calculate aerodynamic drag. Also mustang dynos have what is called an eddy current load cell. This is basically a magnetic brake. This brake is strong enough, it could basically stall a Peterbuilt. The eddy current applies a certain amount of brake against the drum, it measures this resistance along with the drum rpm over time, rpm of engine over time and the entered aerodynamic drag. All of these factor together to create your dyno chart and numbers.
A dynojet dyno is usually inertia based, some are actually eddy current dynos and function like mustang dynos. The inertia based ones calculate power by the acceleration of a known mass over time. Basically on typical dynojet, you have the drum which usually weighs somewhere around 2500 lbs. Say your car is able to accelerate that drum from 100 rpm to 300 rpm in a certain time while gaining a certain engine RPM, the dyno will use these to create the power numbers and the graphs.
There is no correction factor that one has over the other. Most of the time, you will get a dynojet or comparable number. It's important to remember that not all dynos are calibrated the same way. I have personally witnessed a car put down 480 rwhp on a dyno (same one I had my Z28 on) then complain that it's supposed to be over 500 rwhp as a package. He takes that car the same day across town, and magically puts down like 540 rwhp. I have also seen guys struggle to break 400 whp, zip across town and magically their car puts down 420+ whp.
Typically an eddy current dyno is best for tuning, an inertia based dynojet is great for numbers, except on a turbo car. They inertia dynos can't load the turbo cars to get proper spooling.
99 Chevrolet Camaro Z28 M6 - 6.676 @ 103 in 1/8, 10.512 @ 130.2 on street tires, H/C/I
93 Eagle Talon TSI AWD 5spd - Built 6 Bolt, 16G Evo3, HKS 272 Cams - under construction
94 Mustang GT - 5.0 bored and stroked to 347, Vortech V1 @ 10 PSI, Tremec TKO 600 - PIA