Today, we'd call them grousers. Back then they called them "spuds" because they looked like a shovel you would use to dig up potatoes. They were attached to th top of every forth or fifth track link for extra traction.
One and the same...that is the handle of the shovel. If you look close, you can make out the spade portion.
They don't, because of the angle the photo was taken. You don't see the gap between spuds, so it appears that the track is continuous. However, it is not.