What is the role & behavior of capacitor in ac and dc circuits Types of Capacitors: It is same function or not

It is not the same in AC and DC circuits. Read this.
Difference Between AC & DC Capacitors

I think what you may mean by AC/DC capacitors is that an AC capacitor is not polarized and can store energy in either direction. A DC capacitor is polarized and will only store energy when connected properly... otherwise it could blow up.