A supercharger is a compressor driven by the engine rotation (belt driven) whereas a turbo charger is driven by exhaust gas pressure.

But then both force air/fuel mixture into the cylinders.

A turbocharger is a device that uses the force of the air leaving your exhaust to spin a fan (turbo). That fan then pushes more air into the intake and provides a more ideal air/fuel mixture for a better combustion, that then provides more power. A downfall to this is that you need to build enough pressure with your exhaust to properly activate the turbo in order for you to increase your power to the engine. This is often referred to as "turbo lag" and can be avoided with a valve system (often called a "turbo lag delete" kit) that always provides a reserve of pressure to be accessible as soon as you start to press on the gas pedal.

A supercharger, however, still provides that "boost" of air/oxygen into the air intake, but it uses a mechanical system to pwer it. Usually it is driven by a belt attached to the engine, kind of like your alternator or cooling fan, but can also be driven by an electrical motor. Since this supercharger will always be turning along with the engine, there will be no delay in added power, or "lag".

In most cases a supercharger would be preffered for performance, but a turbo tends to be easier to install on most engines and can be more versatile.

There are many technical differences but I think the main one is how they're powered.

For those who don't know, both are devices used to get more air into an engine. When working properly, air mixes with the fuel to form a delightfully explosive mixture which pushes the piston in the cylinder during the power stroke to keep you rolling down the highway. Without the air, if you just added more fuel to the engine, the fuel wouldn't burn as efficiently and you wouldn't get the increased power that you were expecting when you stomped on the gas to get past the geezer in front of you. Normally the air is sitting around the carburetor or intake manifold only at atmospheric pressure so even though you can move the piston really fast to create a big vacuum in the cylinder, the amount of air that can move into the cylinder during the time that the piston is moving is limited by the pressure it's under and may not be enough to burn the amount of fuel you're jamming in there with your giant new fuel pump and fire hose sized fuel lines. So what you do is, you use a fan to blow more air into the engine. (I'm using the term "fan" just to refer to the thing that pushes air around.)

A turbo charger is like two fans connected by a shaft through a barrier. (Here's a text drawing: X--|--X where the Xs are the fans, the -s are the shaft and the | is the barrier keeping the intake and exhaust apart.) One of the fans is in the engine exhaust stream and as the exhaust leaves the engine it spins the fan and the shaft. The fan on the other side of the barrier is connected to the shaft so it spins and forces the air into the engine. Remember, the exhaust is leaving the cylinder under the pressure caused by the ignition of the fuel and air mixture plus the piston clearing the cylinder during the exhaust stroke so the exhaust gas can be moving at a pretty good rate and have plenty of energy to spin the fan when the engine is really revving up. At lower RPM there is less energy in the exhaust stream which means the fan at the other end of the shaft isn't spinning as hard so the turbocharger doesn't have as much of an effect.

A supercharger is also a fan but is not powered by the exhaust gas. The fan in the supercharger is powered often by the engine itself but since that takes power that could be used to turn the wheels the fan may be powered completely separately by an electric motor or something. Supercharger fans don't usually look anything like what you'd normally think of when you think of a fan but the effect is the same, to get more air into the engine. Supercharger "fans" are extremely specialized devices designed to get as many air molecules into the engine as possible and usually create very high pressure.

Or something like that.

They are both “superchargers”.

A “supercharger” (the “super” part means “above”) compresses the intake air (the charge), generally through some mechanical connection to the engine such as a belt drive. When the exhaust gasses are used to power it the word “turbo” (because it uses a turbine) is added; but then in common usage the word “super” often gets dropped.

Fun fact: a turbocharger IS a supercharger. They were originally called turbosuperchargers, but eventually just got shortened to "turbocharger" or even "turbo".

Superchargers can be belt driven, gear driven, driven by a separate motor (electric or internal combustion), or (in the case of the turbocharger) by the residual energy in exhaust gases. They all perform the same function: they force more air into the engine to make it more powerful, but each method has different advantages and disadvantages.

When it comes to phone chargers, different cell phone manufacturers have different charging standards and some let you charge at 65 watts or even up to 200 watts to charge a device from 0 to 100 in 20 minutes.