Why are both the Roman Republic and the United States today considered republics?

Why are both the Roman Republic and the United States today considered republics? They are both the region where the citizens vote to pick the leader(s) who make decisions. A city conquered by Rome might become a Riman ally.

legislative branch:

one of the three branches of government divided between the senate and the house of representatives.

- creates or makes laws

- power to override a veto

executive branch:

one of the three branches of government, headed by the president.

- enforces or carries out laws

- power to veto a bill sent to it by congress

judicial branch:

one of the three branches of government, headed by the chief justice of the supreme court.

- interprets laws

- power to declare laws or actions by the government unconstitutional