Even Lenin, of all people, argued in favor of a (regulated) market economy.

It's a weird of inverse no-true-scotsman argument. I haven't met many socialists who argue in favor of a fully centralized economy. The big discussion, I suppose, is how much should be regulated, and which parts of our society should be 'markets'.

Don't bother, the rose emoji socialists in this country don't know the difference between socialism and social democracy.

Not the real definition, but the definition in most americans' heads. Many probably also conflate those with communism.