Genus and Species. At the final levels of classification, in which the Southern magnolia is identified as a unique species, there is a two-part scientific name. The first part of the name is the genus, and in the case of Magnolia the genus name and the common name are the same.The species name is “grandiflora,” referring to Southern magnolia’s usually large and showy blossoms.lthough conifers, such as pine trees for example, produce seeds, they are not flowering plants. The Southern magnolia, however, is a true flowering plant. It shares this classification with other magnolias and a broad diversity of many familiar flowering plants in the division Magnoliophyta, the flowering plants.