There is no DC to AC or AC to DC conversion going in either of the circuits. In fact the idea behind this is to isolate the low voltage circuit (which operates on low voltage DC) from the high voltage light (or whatever you have on the 120v side).

The first circuit is simply a switch that you can use to turn on an off a high voltage circuit.

In the first circuit ( low voltage switch circuit), Is it an AC to AC converter or AC to DC convertor??

Here is a good explanation of a capacitor – http://en.wikipedia.org/wiki/Capacitator

In the case of my circuit – The capacitor is is charged by the blinking circuit. That charge takes a little time (milliseconds) to dissipate out of the capacitor (think of the capacitor like a battery with a really short life). If the capacitor was not in place the 120v light would go off immediately when the blink circuit was not powering the MOC3020M. The delay created by using the capacitor affects the blink rate of the light.

In reality the capacitor on the switch circuit is not necessary – you could simply adjust the timing of the blink circuit. I had the cap in place already so it’s important to note that if it’s eliminated the blink rate will be affected.