Ahhh, but do you know where the name comes from?
Tunicates have a stiff "coat" or "shell" that protects their body. A "tunic", if you will.
And to spoil the wonderful beginning of SEFs writeup, it's not actually going back through the family tree, since all organisms that are still alive now have evolved as much as we have. It's more like having a distant cousin that is a professional wrestler, a wino, or a congressman.