IIRC (when I was in 5th grade, someone brought in a few pieces of sugar cane to show the class -- 5th grade was a long time ago!), sugar cane is about an inch or so thick, and it's the inside that's refined into sugar. The outer woody (again IIRC) husk or rind or whatever I think is what Brazil makes into ethanol.
In any case, from what I read, sugar cane is a much better source for ethanol -- produces far more energy per pound (or whatever the appropriate measure is) than corn.
I believe you are correct. I watched a show on NatGeo about how they made ethanol from the sugar cane in Brazil. IIRC, It does not effect the sugar used for food, and it does yield way more ethanol that corn.