Do periods stop even if you're on birth control pills?

With the traditional Birth Control pill you take a cycle of pills every day for 21 days and then 7 days of sugar pills. In the 7 days of the sugar pills you have a period. Today, there are pills that skip the 7 days of pills and you stay on pills for 3 months and then after the cycle of 3 months you have a period. In both cases after the period you start a new cycle of pills.