Answer:
The term republic comes from the Latin 'res publica', public thing, the public subject and therefore from everyone.
This regime of government was discussed by philosophers like Plato, and several scholars have gone over to explain what characteristics the Republic should possess.
Initially, the Republic would be a regime of government in which all citizens were called to participate and make their contribution to the common good. This would only be achieved through the development of values such as justice.
Presidential republic
The Head of State and the Head of Government are the same person, and can be elected both indirectly and directly. In this way, the job entails a huge responsibility and to take it off the job is a huge cost of time and energy.
Examples of presidential republic with direct vote: Brazil and Argentina.
Example of presidential republic with indirect vote: United States.
Semi-Presidential Republic
In this system, the prime minister and the president live together. Unlike the parliamentary republics, here the president is the Head of State and Government and the prime minister is chosen by the agent.
Th prime minister acts as speaker of the interests of his party and the president before the legislature.
In the event of a crisis, the prime minister may be dismissed by Congress or by the president himself.
Examples: France, Portugal and Egypt.
Parliamentary Republic
The Head of State is the president, elected by popular vote, but has no effective powers. His role is limited to crisis cases and acts as a representative of the country abroad.
In turn, the Head of Government is the prime minister who is elected during the legislative elections.
Generally, the prime minister is the deputy who topped the list of candidates from the most voted party in the elections.
The prime minister can be fired at any time, especially if his government is not pleasing his party coalition. Also if the opposition gets the votes needed to overthrow the government.