When an individual is referring to the fungi kingdom, fungi is the correct scientific name for all of the organisms that are classified as fungi. The kingdom fungi may be broken down further into sub kingdoms, phyla and subphyla.
For example, the phylum chytridiomycota contains some of the earliest evolved fungi. Another phylum, zygomycota, consists of land dwelling fungi that only have septa in reproductive areas. The phylum ascomycota includes yeasts and molds.
Each species of fungus has a scientific name. Amanita flavoconia, a species of mushroom, is a part of the order agaricales and the phylum basidiomycota, in addition to the kingdom fungi.