Centrifigal Usually looks like a turbo, With a pulley on the back which turns the compressor whell according to the engines RPM, the more RPM the more boost that can be made and is forced into the Engine by a intake pipe.
Twin Screw, Roots, Take the place of the upper intake and using 2 compressor wheels that look like twizzles candy next to each other, they literally screw the air downward into the engine. Again Pulley driven so according to Engine RPM is the power they will deliver.
Turbocharger, My personal fave, this is exhaust driven, There are 2 compressor wheels on a shaft inside the turbo, The exhaust air passed through one which turns the other, The other is what blows air into the engine,
Thats the shortest explanation,
If you want a more in depth guide with visual aids go to howstuffworks.com and look in the auto section.
Turbo is my FI of choice too. Just one clarification though: Technically, the roots type (positive displacement) blower isn't a compressor, as it simply takes the air coming in the top and blows it down into the engine. A twin screw takes the air coming in the back of the case, and compresses it as it "screws" it to the front and down into the engine.
Breakdown:
A centrifugal compresses air internally, and is better designed for high boost, high rpm applications. (think drag racing) The turbine has to spin astronomically fast, so the tollerances allowed in production have to be more exact than the others, with almost no parasitic drag.
A roots type is literally a blower, and the compression takes place in the intake manifold ports. Less mechanically and thermally efficient, but makes huge low end torque right from idle. Very fun in a street car.
A twin screw blower produces the same nice flat torque curve early in the rpm band that the roots does, but is far more efficient, quieter, better hood clearance, but is usually more expensive. It is typically easier to make higher boost levels with them than the roots type.
Yes and no. The Cobra has the same Eaton M-112 blower that the Lightning has, which is a roots type. However, unlike the Lightning, it has been modified to have a rear entrance for hood clearance purposes, making it a kind of hybrid. It isn't a twin screw, but it does have some of the increased efficiency of one. Right now the hot mother of upgrades for the Terminater is the Kenny Bell twin screw blower, which can spin up more than 20psi of boost. You'll never get a stock Ford Eaton M-112 to do that, the rotors are still different inside and there still isn't a whole lot more compression in the blower itself. So theoretically yes, kindof; technically no.