It sounds like Devil's Food Cake, which also uses beet root. I made a similar cake a few weeks ago, with the beet roots and everything, and I was totally disappointed, because it was completely tasteless. I hope your recipe is better than mine :)
"Is there a difference between beetroot and beet? We can get fresh beets and tinned ones, but I don't believe I've ever seen anything labeled beetroot."
A fresh beet is a beetroot. They come attached to the stem in fancy grocery stores. Just cut off the greens, wash the roots, and toss them in the cuisinart, and oila, grated beet root. In cakes like these, their prime purpose is to provide coloring, as you'll note they have a deep purple color.