Here's the thing, while I think your argument has merit, I think it's not the topic that we're discussing here. I seriously doubt anyone is promoting the elimination of private property these days within the West or Europe. To play the pedantic game here may not be relevant, when even the dictionary has equated the two - rightly or wrongly. I know neither Sanders nor Occasio-Cortez, nor the Canadian NDP advocate the elimination of private property, and in Europe these people are just referred to as Socialists and lumped together.