I just realized...stupid me. Yes, you are right. I didn't realize you were talking about the same tree. According to wikipedia, these are all of the common names, together with the northern whitecedar and the eastern arbovitae: Tree of Life, Yellow Cedar, American Arborvitae, Arbor Vitae, Atlantic White Cedar, Cedrus Lycea, Eastern White Cedar, False White Cedar, Hackmatack, Lebensbaum, Thuia du Canada, Thuja.