ardilla:
What's the difference between these two?
Simplified, a capacitor is a barrier for DC and a pass through for AC.
C1 acts as a buffer, so that one is understood correct.
C2 is an AC pass through, and will never be used as drawn (to a power supply connection).
One would connect one side a a capacitor to some signal and the other pin to some input connection if one wants to make sure they are only receiving AC signals.
Read AC as continuously changing levels in this case.
Again this is very simplified, and there's much more to be said about this.