As it happens, most people assume ‘order by people’ to mean order by the masses or the public-at-large, but there is not such magnitude provision for democracy. Ostensibly, it’s just people ruling people.
Historically, it is used to differentiate between anarchy, monarchy, oligarchy, and so on—though to be fair, save for anarchy, all of these involve people ruling people. And even anarchy is people exercising individual sovereignty.
Democracy’s Athenian origins had citizen-people ruling in a direct democracy. The catch, is that the definition of citizen excluded the majority of people—women, slaves, persons younger than 20, and so on—, so clearly it was not intended to be all-inclusive.
Another people-oriented order is demarchy—rule by the randomly selected. No modern country has ever adopted this form of government, but it should be noted that randomness has been used as part of selecting leaders in the past. Sortition, another term for random selection, was used for a hundred years in ancient Athens to choose members of the legislative council.
To be honest, given the political climate—at least in the United States —, random selection feels like a better alternative to the current system of meritocracy [sic].