Differences between presidential and parliamentary republics?

A parliamentary republic presupposes the election of the president by a parliamentary majority, and not by popular vote – as in a presidential republic;
In a presidential republic, the head of state has much greater and wider powers than in a parliamentary one; in a presidential republic, the head of state is elected by the chairman of the government and various ministers;
In a parliamentary form of government, these officials are elected by a special parliamentary apparatus.

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