Of course, there have been many different religious leaders and political leaders in different times and places so we can't just say that there is one way in which each of these types of leader tries to control their followers. In general, religious leaders and political leaders have used many of the same tactics, though political leaders lean more towards coercion while religious leaders use persuasion more.
Religious leaders tend to try to persuade their followers by arguing that they must do what is right. They use moral arguments to try to get their followers to obey. However, they will sometimes use force. Catholic popes often used the power to excommunicate as a way to try to force obedience. There was also the use of the Inquisition to root out "wrong" belief.
Government leaders tend to use force. They have the power of the police and the military behind them to enforce their will. On the other hand, they too try to persuade. They use appeals to patriotism and to ethics and morals to try to persuade their people to follow them as well.
One way is through deception. When the Bible was compiled, certain texts were omitted in an attempt to control how much knowledge was available and to make several religions more compatible, enabling them to control the masses more effectively.
Our government, that we see as reality, is in fact/theory (You decide) run by secret societies ( the Illuminati, Freemasons...) that are globally connected. Yet another facade.
Just a little food for thought, and maybe some areas for further research on your part.