Oddly enough, a ponytail palm tree is neither a palm nor a tree. In fact, it is a member of the Agave family and is actually a succulent. Other common names for this plant include the bottle palm tree or the elephant foot tree. In the past, it has been classified as either Nolina recurvata or Beaucarnea recurvata, but the latter is now the correct classification of this plant. The common characteristics of this plant include a bulbous trunk, which is used to store water, and its long, hair-like leaves that grow from the top of the trunk like a ponytail, giving the plant its renowned name.