It can get confusing. Whats going on here is the crossing of 2 species, with different 'cultivar epithets'. Thats the name in the quotes. If a grower raises a batch of plants that have outstanding / different qualities than others of its type, he/she may want to get it registered. Thus, giving it the cultivar name.
So, using one of your examples... Paph. delenatii ('My Fair Lady' x 'Irene'). This is 2 species paphs, one registered as My Fair Lady, the other Irene. If you and the other poster, Snow had delanatii cultivars named after yourselves, you could make a cross called Paph delanatii 'Helen' x 'Snow'. Still a species, as long as the same species is used in the cross.
Robert Bedard Horticulture : Orchid Nomenclature
Cultivar - Wikipedia, the free encyclopedia