These are hybrid epiphytic cacti often called "Epiphyllums." Strictly speaking, this is not what most of them are! Epiphyllum is only one of a number of epiphytic cacti species, and have been interbred with other epiphytic species such as Nophaloxcia, Selenicereus, Heliocereus. The resultant plants are known scientifically as "bigeneric hybrids," and are not "true" epiphyllums. However, for convenience the commercial producers of these hybrids have tended to call the hybrids Epiphyllums, and this is how they are commonly known.
Given that "epiphyllum" is not really appropriate for the hybrids, we call them "epicacti" (epiphytic cacti) to distinguish them from true epiphyllum species.
Various seedlings we have grown on, and in some cases used as parents for further crosses if they have valuable characteristics such as form, color, flower longevity, hardiness, disease resistance for example.