I know both Sophronitis and Laelia are part of Cattleya alliance, but without being too technical are the basically the same? I have a Bl. Morning Glory x L. purpurata cross and Orchid Wiz keeps bringing up S. purpurata when I try to find out if it's a registered cross. Would that be the same thing, just part of the "name change game"?
This is part of the current "name game" as you indicate. Brazilian Laelias were lumped into Sophronitis by taxonomists which put the Cattleya world upside down from traditional terminology. Just be prepared for the next lumpage into Cattleya - the names will change again.
Another change that will be reflected soon is the lumping of Odontoglossum into Oncidium. Pretty crazy stuff for traditionalists.
Unfortunately, name changes will always come up for valid scientific reasons, and are happening a lot right now as genetic analysis begins to have a big effect on taxonomy. But there is absolutely no reason that traditional names can't continue to be used for horticultural purposes. Keep your old tags rather than trying to keep up with the bleeding edge of science as the RHS is trying to do.
This is a interesting one because there is 2 Morning Glory's, the first one (I think this is yours) is Brassocattleya Morning Glory, the parents being Brassavola nodosa x Cattleya purpurata, ( yes purpurata is now a cattleya), the second one is Catyclia Morning Glory, parents are Cattleya Issy x Encyclia cordigera. Hope this is of some help.
Warren