Dylan Matthews has a short post on equality of outcomes versus equality of opportunity. Political rhetoric claims that you can't choose one or the other. In the real world, though, it turns out that
the distinction between equality of opportunity (usually phrased in terms of upward income mobility) and equality of outcomes (the raw distribution of income or wealth in an economy) is not as big as it sometimes appears. More specifically, countries with high inequality of outcomes (as measured by the Gini index of economic inequality) tend to have low social mobility (as measured by the association between parents’ and childrens’ incomes) as well….
The distinction between equality of outcomes and opportunity has some theoretical appeal, but in practice, you get both or neither.