Polish barszcz is not traditionally made with cabbage - it's at heart a beet soup. Some variants of the soup made in Ukraine or Russia may contain chopped vegetables and sour cream, but in Poland warm barszcz is a consommé-style soup. There is also a cold variant served in the summer called chłodnik (a literal translation of which would be something like "cooler") which has sour cream in it.

Cabbage soup is called kapuśniak (from "kapusta" which is cabbage). Żurek is a fermented rye soup often called "white borscht" on North American restaurant menus. Another Polish soup worth trying if you find it on the menu and like sour flavors is zupa ogórkowa, which is a dill pickle soup.