Couple things: tiered income would likely exist in early stages of Communism, and certainly in almost all forms of Socialism. Marx makes it exceptionally clear that both intense and skilled labor are represented as condensed unskilled labor.

Either way, there are examples of anti-capitalism. Chiapas and Rojava are more Libertarian Socialist. There's also countries like Cuba, Vietnam, and Laos, who appear to be attempting to reject Capitalism still and still operating on some basis of Marxism-Leninism Socialism. China relies on Capitalism as their dominant mode of production, but claims to be Socialist by 2050, though that remains to be seen.

The nations you think of as "Communist" are typically Communist in ideology, but are building towards it through Socialism. Just as Feudalism gave way to Capitalism, so to do Marxists believe Capitalism is a necessary stage before Socialism, which is a necessary stage before Communism.