A capacitor is a capacitor, no matter what circuits you use it in. There is no difference between one used in AC and one in DC, except perhaps the size that is appropriate.
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to limit the current and to use it as a back up battery capacitors are used ..
A time activated switch could use pneumatics or an resistor capacitor circuit.
You use a capacitor to store electrostatic energy. You use an inductor to store electromagnetic energy. You use a resistor to dissipate electrical energy.
The shape of a capacitor has no meaning to the circuit. What matters is the capacitance, the voltage rating, and the current rating. 35uf is not the same as 45uf.
A polarized capacitor is one which has a polarity, positive on one terminal, negative on the other. This makes it superficially look like a battery. In use, the capacitor has its positive voltage always higher than that on the negative terminal, it matters that this is the case and this gives rise to the term polarized. This sort of capacitor is commonly found in power supply filters.