Nowadays (for the last few hundred years) borshch is basically a soup made with beets being the main vegetable ingredient, so there are different types. In Poland, the most popular is Ukrainian borsch which uses a variety of other vegetables too, but there is also Polish borsch that is clear, you can think about consomme based on beets, and you can add dumplings or a savory pastry on the side. There is also cold borsch made with beet leaves (called Lithuanian cold soup), great in summer. Russians have some types of borsch too, but my only experience was ready-to-eat "Moscow borshch". I am not aware of any Czech or Slovak borshch.
Originally, borshch was based on leaves of a plant with that name, these plants often grow to be huge weeds and could be used as food when crops fail -- and as a soup ingredient in happier times.