There are two types of democracy government-direct and representative. In both types, the citizens have a say in their government and they have several rights including the right to vote. Citizens elect their representatives by voting, once they can legally, in a representative democracy. In a direct democracy, every citizen who can legally, votes on every choice made in the government. Other rights in a democracy are the freedom of the press, petition the government, assembly, speech, and religion. Even if the citizens do not agree with the president's beliefs or choices, the majority rules in both a representative and direct democracy.
In a theocracy, the leader is believed to be God or chosen by the Gods. The Holy book is the law. This type of government usually goes with another type (typically dictatorship and the leader of the theocracy has unlimited power.) The leader's power (limited/unlimited) depends on the type of government that goes with the theocracy.