A coworker from several jobs back who had some part of her ancestry somewhere in eastern Europe insisted that "borscht" just means "soup" and does not imply beets at all. She made vegetable soup with no beets that she insisted was a folk recipe for borscht. So the universe of borscht may be even wider than you thought, since all of the different forms with beets are found in the "beet borsht" corner.