The alternator is what produces the 12-14 volts to power the elelctrics in the car and to charge the battery when the engine is running. The coil is effectively a step up transformer. It takes its feed from the alternator, steps the voltage up to about 12000 volts (i think thats about right) which is what is used to produce the spark at the spark plugs. You will notice that on your car there is a lead that runs from the coil, to the distributor. The power is sent from the coil to the distributor, then from the distributor down the 4, 6, 8 or 12 spark plug leads to the spark plugs themselves.
A faulty coil would mean that the plugs arent sparking properly...which is why your car is a nightmare to start in the mornings.
Hope that makes sense!!