When I think of a tube pan, I think of the kind of pan that an angel food cake is made in. It does have flat sides, and some actually have two pieces (although not all of them do). The one my mom used did have two pieces. One piece consisted of the sides with a slight rim on the bottom. The second piece was the bottom with the center "tube". The bottom sat on the rim of the first piece. Does that make sense?
I think it was/is easier to remove the cake from the pan in one piece if you used the two piece pan, because you could slide a knife around the sides of the cake and take the round side piece off, then you could slide a knife under the bottom and around the tube, and remove that piece.
I have seen recipes that call for one pan, but then say the other can be subbed, so I don't think it matters unless you prefer one look over the other. (Flat sides over fluted or vice versa.)
Less rhetoric, more cowbell!