I agree with what you say above in both instances except a civil society is actually cosmopolitan (it includes strangers). It is where civil actions of reason and peaceful discourse are occurring and that can be anywhere, but it definitely doesn’t include everyone in any given decision making process. You can look around yourself and see the civil society now (except if ex.: crime is occurring, but if justice is working, then harmony is remaining relatively intact). You may not know the people you view or hear about in the region, city, town, farm, or family, but if civility is happening then a person can say the society is being civil. Here’s how that paper I quoted in the OP defines civil society:
“In Aristotle’s polis, politics involved discourse and deliberation between equals in joint pursuit of eudaimonia. Aristotelian politics is not possible in modern democratic and non-democratic states. I will also argue that politics presupposes liberty and therefore the proper locus of politics is civil society, not the state. My account of an explicitly non-statist, eudaimonist politics is to my knowledge unique, although it does receive its inspiration from several disparate sources: Aristotle, libertarian market anarchism, and the New Left. It will aim to show how politics and morality are intimately related but nevertheless that true politics presupposes liberty and so libertarians need not worry that this opens the door for state intervention.”
Further:
“One of these is that Aristotle conflates the state and civil society in his conception of the polis, a conflation that might have been unavoidable in the era of the Greek city-state but can no longer be excusable in light of modern experiences, theory and historical knowledge. The conflation of state (an organization) and civil society (a spontaneous order) can only lead to conceptual confusion, paternalism and totalitarianism.”
One more:
Ronald Hamowy has observed that “For at least two hundred years [owing to the Scottish Enlightenment], social philosophers have known that association does not need government, that, indeed, government is destructive of association.”10 Scottish Enlightenment thinkers like Adam Ferguson, David Hume and Adam Smith as well as modern thinkers like Austrian economist F.A. Hayek have theorized about and described the emergence of society, culture, law, language, and markets as spontaneous orders. Austrian economists, libertarians and others have built up a significant body of literature that demonstrates both theoretically and historically that legislative law and state-provided goods and services are inferior to other institutions in civil society: free markets and free enterprises, cultural norms, customary law and polycentric legal systems, and private organizations such as the family, churches, private schools, clubs, fraternal orders and the like."
Civil society is the spontaneous order of individuals associating. It is defined in that last quote as “…civil society: free markets and free enterprises, cultural norms, customary law and polycentric legal systems, and private organizations such as the family, churches, private schools, clubs, fraternal orders and the like.”