The difference between a left-wing and centrist liberal is that left-wing liberals focus on social equality while centrists focus more on economic freedom.
Left-leaning liberals strive to create fairness in society through promoting income and wealth redistribution as well as other progressive taxation efforts, while centrist liberals tend to be content with maintaining the status quo when it comes to inequity but are more intent on reducing government size and minimizing economic restrictions. In both cases, Americans believe liberalism will solve the problems they’re facing; but because of their different views, this seldom happens.