Exactly, a real cape is like a blanket that you wear.
Some (traditional) hunters in Austria, Germany, Czech Republic, etc wear them, especially when sitting on a stand or in a raised blind. When you're back at the lodge you can take off your cape and the dog can sleep on it, or you can throw it across your lap like a blanket. These are most often loden cloth.
There is also a formal cape. When wearing a coat with tails (either a cutaway morning coat during the day, or a white tie tailcoat at night), a cape is the more appropriate overgarment than an overcoat. Something to do with standing and sitting. You'll notice that in many pictures of Woodrow Wilson and FDR, when riding around in an open carriage or automobile they would be wearing a heavy dark wool cape. An opera cape for night would usually be lined in silk.
FDR was so famous for cape wearing that he was memorialized in one. I came very close to buying a cape, but forgot about the ebay auction. Sadly the cape era is over