A people is a plurality of persons considered as a whole, as is the case with an ethnic group or nation. Collectively, for example, the contemporary Frisians and Danes are two related Germanic peoples, while various Middle Eastern ethnic groups are often linguistically categorized as the Semitic people. See the list of contemporary ethnic groups for more examples.
Various republics govern, or claim to govern, in the name of the people. Both the Roman Republic and the Roman Empire used the Latin term Senatus Populusque Romanus, (the Senate and People of Rome). This term was fixed to Roman legionary standards, and even after the Roman Emperors achieved a state of total personal autarchy, they continued to wield their power in the name of the Senate and People of Rome.
A People's Republic is typically a Marxist or socialist one-party state that claims to govern on behalf of the people. Populism is another umbrella term for various political tendencies that claim to represent the people, usually with an implication that they serve the common people instead of the elite.