Both setups mix the fuel before the cylinders.
A carburator is a purely mechanical device. It uses the vaccum created by passing air to suck gas out of a small needle valve. The more air flows (Volume, not Mass) the more gas is sucked. They often do not require a fuel pump, also most bikes have them. Some carbs have several needles for different ranges, etc, etc.
A fuel injector is a small sylanoid (sp?) valve operated by a computer. It opens in pulses, and injects a certain ammount of gas, ussually directly into the port (at least on sportbikes). In order to inject a properly calibrated ammount of gas the fuel rail has to be under exact pressure, commonly 50psi.
The difference is that a carburator responds only to the volume of air, thus if the density of air changes, it cannot compinsate. FI uses sensors to inform the computer about those things.
The biggest difference to the owned is tunability. Carbs can be tunes with a screw driver, and some vaccum gages, where as FI needs a computer. However FI produces much more accurate results.. Cheaper to tune too...