a tale of two privets

Sometimes a tree is so ubiquitous you don't even notice it. Circumstances have recently brought a new one to my attention: Ligustrum lucidum. My first impression was that it was some sort of Ficus, with glossy leaves and bony, reptilian bark, and white flowers in dense clusters that become bird-friendly, dark-blue berries. In fact it's in the Olive family, and goes by the common names of Tree Privet or Glossy Privet. This is confusing because when I think of Privet, I think of hedges back east that also go by that name. That one is Ligustrum vulgare, coming from Europe, whereas lucidum comes from Asia, the latter having proven to be invasive. But they are all Ligustrum and therefore all Privet.