Actually, looking it up they aren't close relatives (turnips and swedes are Brassicca, so they are closer to cabbage and Brussels sprouts). But to me they are similar, and a number of cultures use the same names for them (in particular I've heard rutabaga used for beetroot as well as for swede) and refer to the whole lot as 'beet' or 'turnip'. Swede is still quite popular as a side-vegetable in England with a roast meal, a typical pub "Sunday lunch" will often include it.

I like beetroot cooked and cold (and /not/ soaked in vinegar!). Or hot in borscht (mmm, borscht!). It's messy to cook, because the juice stains anything it can find and is almost impossible to remove.