gazebo: A small, covered open-air pavilion with a view.

pergola: An overhead wooden garden structure supported by evenly-spaced posts and often covered with vines or other shade-producing plants. Also known as an arbor.

So you could call it a gazebo OR a pergola. Really its probably more of a pergola (and besides, gazeboplans.com was already taken).  Oh well, who cares what you call it!  Since its such a unique structure, its just hard to categorize it.  Actually, as shown here the TRADEWINDS is more of a SWING STROMBRELLA, made for this lovely hammock swing, available from NAGS HEAD HAMMOCKS. The roof is make of 2 x 2 slats, perfectly blended together at the corners. Whatever you want to call it, THE TRADEWINDS is one of the most elegant and unique garden structure designs you'll find anywhere!