Well sort of. Each of those are general terms for a group of species that are generally compatible with each other to make hybrids. For example, the Oriental lilies (garden hybrids) may have species such as Lilium auratum, L. japonicum, and others in their background. Same with the others, Asiatic, trumpet etc. So you can see by the time OT lilies come along it is quite a mix up!
We will have Lily Week in July and will likely discuss all of this stuff!