I'm tempted to dig out my books from college to prove a bunch of people wrong... however I don't have a great enough desire... I will however post my knowledge and anyone who wants to flame me can go ahead and make an ass of themselves, and those who can respect my opinion and have enough faith that I wouldn't spout off crap I don't know to be true, are welcome to comment/ask questions.
Turbo charging and Supercharging are both methods of forced induction. Forced induction is exactly what it sounds like... air is forced into the engine.
A naturally aspirated engine draws air in when the intake valve is open and the piston moves down in it's bore, creating low pressure, which causes atmospheric pressure to fill the low pressure area. This is where the argument comes from about whether air is forced in or sucked in... which will come up later in my explanation of superchargers.
Forced induction is using a device to force air into the cylinders, rather than letting the air flow in naturally due to the vacuum created. This is where the term "blower" came from... air is blown into the engine.
Turbochargers accomplish forced induction by using exhaust gasses to spin a turbine that is connected to another turbine by a shaft.
For simplicity, I'll call the turbine that exhaust turns the driving turbine, and the one it's connected to the driven turbine.
At a normal idle speed, about 800 RPM, there is not enough exhaust gasses exiting the engine to spin the driving turbine with much force, so not much boost is produced... when you increase the engine RPM, more exhaust gasses are exiting, thus increasing the driving force on the driving turbine, and also the speed of it.
The driven turbine is spinning also, and is drawing air in and forcing it into the engine... when more air is being forced in than the engine normally could draw in on it's own, you start to see increased power, which spins the engine faster, moving more air, which drives the driving turbine harder and faster, which spins the driven turbine faster, which forced even more air into the engine and will eventually increase the pressure above atmospheric pressure. This is the point at which we say it is creating boost, measure in PSI.
A turbo charger also uses something called a waste-gate, I'm sure you've heard the term before. The simplest way to explain a waste gate is to call it a pressure relief valve. In it's simplest form, it is operated by a spring, and when the turbo charger creates a certain amount of boost, it overcomes the spring pressure, opening the valve (waste-gate) and relieving some of the pressure. This is necessary because if you allowed it to build up as much boost as possible it would damage the engine in one way or another. (What way isn't really important, but if you want, I can explain some different ways.) When you have a car with a turbo charger that creates a lot of boost, you hear a sort of hissing sound when the car is shifted. This is the waste gate opening as the RPM of the engine drop, which reduces the airflow through the engine, which will create higher pressure in the intake system... so the waste gate opens to bleed off the excess pressure to prevent damage to the engine and turbocharger.
To my knowledge, the only reason turbo chargers are more efficient is due to the lack of frictional losses, being only a couple moving components. Although, when compared to certain types of superchargers, they don't heat the air as much, and cooler air is denser, so you can make more power.
There are several types of superchargers.
There is the roots style, which most of you think of when you think of superchargers. They're the large ones that sit on top of the engine, with a carburetor on top, and often some sort of scoop. They use rotors that mesh together and compress the air as they turn. Then are pulley driven from the crankshaft and draw air in from the top, and down. These heat the incoming air as well because the rotors create a lot of friction. Hot incoming air is bad for power, which is why these are typically used on low RPM engines with a power band that peaks around 5000 RPM or lower.
There is the screw type, which is similar to the roots type, but use different style rotors that seal better and create less heat from friction. They are also pulley driven from the crankshaft. They pull air in from the front, and back... a design that allows it to use less vertical space, and allow them to be placed under the hood of a car without a large scoop or cowl built into the hood. This is the type used in Ford's SVT Lightning. These also heat the incoming air, but not as much as the roots style due to their more modern design.
Then there is the centrifugal type, which works a lot like a Turbocharger, but instead of having a turbine that is turned by exhaust gasses, and turns another turbine, it is driven by a belt connected to the crankshaft. These mount the same way an alternator or air conditioner compressor mounts. These are the most efficient type of supercharge due to the low drag of the turbine, as opposed to the rotors in the roots and screw type. Of superchargers, these heat the air the least, and most of the parasitic power loss comes from the friction of the belt and pulleys rather than the heated incoming air.
Now, the point I mentioned about whether air is sucked or pushed into the engine...
Roots and Screw type super chargers are between the intake manifold and the throttle plates (whether they're in a carburetor or throttle body, it doesn't matter). This means the air moving through the throttle plates is under the same pressures as in a naturally aspirated engine... and if a carburetor is only capable of flowing 750 cfm at that pressure, it's not going to flow much more even if you create a stronger vacuum. So... to meet the airflow demands of an engine with a roots or screw type super charger, you must increase the area of the venturi or throttle body, whichever you have. That's why you see a lot of roots style blowers with 2 or 3 carbs sitting on top of them.
A Centrifugal Supercharger and a Turbocharger are located ahead of the throttle plates. This means that the entire induction system is pressurized when the device is creating boost. And if the air is under pressure, it's denser, and more air flows past the throttle plates... this is why it's not necessary to increase the size of the throttle body or carburetor as long as it meets the airflow requirements of the engine.
So to simplify the last two paragraphs... in effect, a roots and screw type supercharger make the engine seem like it has a larger displacement to the carburetor or throttle body & computer, so it needs a larger opening for more air to flow through. The centrifugal supercharger and turbocharger, just pressurize the induction system, allowing more air to flow through the same size opening.
** Please excuse any typos... it's late

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