As someone living in Denmark I wonder how do they classify a Danish citizen? Someone living in Denmark, having permanent residence, living in Denmark and being

As someone living in Denmark I wonder how do they classify a Danish citizen? Someone living in Denmark, having permanent residence, living in Denmark and being EU national, holding passport or being born here? Also, from a fair amount of conversation with my Danish colleagues I find it odd how uncritical they are when describing the relationship of Denmark and USA, regardless if I myself find the specific view different than mine. The people in question are of the right political spectrum and not overly political but still.