Detroit marketers over many many years have sensitized us consumers to the merits of horsepower in a car engine. More is better. And for an internal combustion engine, horsepower can actually be measured, with real test equipment, although there are a few fudge factors in the measurement process, like with mufflers or just straight pipes.
Given the success horsepower has been selling cars, makers of all sorts of stuff now advertise their product's horsepower. More is better. And some fairly unbelievable results have been marketed, like the all plastic six horsepower shop vac.
Electric motors carry the wildest claims. Electric motors will put out more and more mechanical power (shaft horsepower) as the load upon them is increased. As the motor works harder, it draws more current, and the current heats the motor up. Somewhere along the line, the motor will burst into flames. As a practical matter, the amount of shaft horsepower you can extract from a motor depends upon how hot you dare run it.
It also depends upon how long you run it. Motors have a lot of iron in them, and it takes real time for the electricity to warm up several pounds of cold iron. For a load that only lasts a few seconds the motor won't heat up much. This principle allows the electric starter in cars. The starter motor only has to crank a few seconds until the engine starts. Then it can rest and cool off.
National Electric Manufacturers Association (NEMA) has a conservative system for rating electric motor horsepower. The horsepower rating is for continuous duty, such as you get turning a fan, or a water pump. For this you get a pretty beefy motor. A NEMA quarter horse motor is the size of a five pound sack of potatoes and weights two or three times as much. NEMA ratings are customary on stand alone electric motors.
For appliances with built in motors, blenders, vacuums, skil saws, and the like, the maker is under no compulsion to use the NEMA rating system. The marketing guys demand the highest possible advertised horsepower, which is the power the motor can deliver in a very short burst. This can be ten or twenty times the conservative NEMA rating. This is how you get a six horsepower shop vac. It's also kinda useless for us consumers when shopping for appliances. In the shop vac case, the highest horsepower rating goes to the machine whose marketing department tells the biggest whoppers. It doesn't go to the machine that sucks the best.