The "Nog" in "Eggnog" is the booze, usually Rum (Dark) or Bourbon to traditionalists. Purists hold to the folding in a beaten egg whites into the basic uncooked custard of egg yolks, sugar and cream (or half & half). Anything made with milk is an imitation, much as "Ice Milk" or "Mellorine' is to real ice cream. I presume that in most available commercial examples (caterers/bars/resturants/hotels), the custard is cooked because of salmonella fears from the eggs, resulting in a product not unlike the 'bottled' offerings on supermarket shelves.
Personally, I prefer the old favorite, "Brandy Milk Punch", not quite as artery-clogging.
I do remember some truly avoidable examples, the bottled Italian (and other "Latin' countries including Mexico) "Uovo" bilge.