This has been discussed before, so I'll be brief
ASM and TCS are 'driving aids'
A turbocharger is a force induction device.
A turbocharger is a device that you will find under the hood a many production cars today. It looks like a snail shell, and can be quite small. This device takes the exhaust from your engine, and uses it to drive a high speed turbine. This turbine forces air into your intake with MUCH greater pressure than normal. You want more air in the cylynder so that you can pump in more fuel, (air/fuel mixtures change with crank speed) which releases greater energy. The more air you can get into your car, the more power you can make, so the bigger the turbo, the more air you push, and the faster you go. There is a bit of lag time between building up enough pressure to boost your engine, and the time you get the effect of the extra air. This is known as turbo lag. The whole setup is very simmilar to a supercharger. A supercharger does basically the same thing, but is driven by a belt.
The effectiveness of a turbocharger is measured in the air pressure it generates, usually measured in bars, or barometric pressure. (the little gauge at the bottom of the screen is turbo pressure in bars) 1 Barometric pressure at sea level is approximately 16 psi. That is that every square inch of ground has 16 lbs of air above it. A normal turbocharger can provide between 6-8 extra lbs of air. These extra lbs of air are referred to as boost. This is a 50% increase in the quantity of air that goes through your intake. It's not a 50% power boost, as other factors play into it though. BIG turbos can put out as much as 2 Bars, or 32 lbs of air. (maybe more) This means that you are putting three times as much air as before into your engine. By putting two of these on your engine, you could run 5 times as much air into your engine. Mucho power. What you have to remember is that the air in your engine is compressed by the piston by your compression ratio. In many cars, this is around 10:1. So if you have 5 bars (80 lbs) of air, plus the 10% fuel (air/fuel ratios vary greatly) your whole engine needs to be able to restrain 880 lbs of pressure per square inch. (big fudge factor here) This is a LOT of pressure.
Not all engines are capable of handling force induction like a turbo or supercharger. All that extra pressure can rip right through the side of your block, cause you to throw a rod, destroy your pistons, or all sorts of bad stuff. Usually, the displacement of engines is reduced by shortening the stroke, spacing the heads, or decreasing the size of pistons. Also, the compression ratio is dropped. The Heads, block, valves, valve springs, (ever see a valve go through a piston, it looks COOL) cams, rods, and crank all need to be prepared to deal with this kind of force. Any imbalance can destroy an engine in half a heartbeat.
The alternative to force induction is Natural Aspiration. This is where the intake stroke of the engine provides a vacuum powerful enough to suck in LARGE quantities of air by simple pressure differential. In both cases, the desire to get more power is fueled by the pressure during the power stroke. Naturally aspirated engines that are designed for power have large displacements, (cylynder volume) high compression ratios, and high revving engines, and more cylynders. (mclaren f1s were runnig around 19,000 rpm last year)
The difference between these engines is not the potential power that it can produce, but how it is produced. The advantage of a turbocharger is that it allows a relatively small engine to produce tremendous power. (the suzuki Escudo has Two twin turbocharged straight 4 cylynder engines to generate the kind of power it has) This keeps weight down which is the holy grail of racers everywhere. Superchargers provide far less boost than turbochargers, but work well on large displacement engines. In addition, small engines have fewer moving parts, and are less expensive and more reliable.
Naturally Aspriated engines can be VERY powerful, but to get the same performance as force induction, they can cost far more. A 12 Cylynder engine is WAY more complicated than a 4banger. They react VERY fast to throttle changes, and have greater torque at low engine RPMs. Most major racing circuits use naturally aspirated engines. (f1, IRL, Nascar, etc)
WHEW,
Deep breath
The driving aids ASM and TCS are methods of computer assisted braking that improve the stability of your car. Stability sounds great until you realize that stability means resistance to turning.
ASM dampens the effect of herky jerky motion by applying the brakes in rapid succession to prevent tires from spinning at different speeds. (such as in a turn) I recommend turning it WAY down (1 or 2) for rear wheel drive cars and off for everything else. Don't use it, less you become dependant on it.
TCS is simmilar to ASM, except that it involves slipping of tires. If you run over some dirt, it has a lower coefficient of friction than asphalt, and so your power goes to the path of least resistance, and causes that tire to spin much faster than the other tire on the axel. Traction contol applys the brakes to fool the transfer case into thinking that the slipping tire is actually the tire on the pavement, thus shifting more power to the tire with good traction. In a turn however, without a limited slip differential, the tires spin at different speeds, with the tires on the outside of the turn spinning faster. Traction control tries to even them out, and ends up widening your turn. I usually turn this off.
Remember, these are controlled from two places, game options and car options, and are by default set at halfway.
Some of what I have said is a simplification, so dont criticize the math too hard, the concepts are right. (I hope)
Enjoy