A Note on Classification
The type of classification used to describe lichens, molds, and mushrooms is called biological taxonomy. This type of classification is sometimes referred to as Linnaean taxonomy, after Carolus Linnaeus, a Swedish botanist who first classed organisms according to their physical similarities. Biological taxonomy incorporates a specific set of groups and subgroups in a hierarchy determined by their scope, from broad to narrow -- the first and broadest classification of an organism is according to kingdom, followed by phylum, class, order, family, genus, and species, in order of increasing specificity. Lichens, molds and mushrooms all belong to the Fungi kingdom.
Lichens
Fungus makes up the bulk of most lichens, except lichens that have a filamentlike or gelatinous structure. Lichen fungus usually belongs to the Ascomycota phylum. Less frequently, lichens are classified in the Basidiomycota phylum, which are filamentous fungi that reproduce sexually. Because mushrooms are classified in the Basidiomycota phylum, some lichens and mushroom both belong to that biological division. Both of these phyla comprise subgroups of organisms that are principally lichens, termed asolichens in the first -- and much larger -- phylum, and basidiolichens in the second.
Molds
Molds, another type of fungi, derive their energy not from photosynthesis but from the organic matter where they grow. Like lichens, most molds fall under the Ascomycota phylum. Because they comprise such a varied class of organisms, different molds can be classified according to hundreds of different subgroups in the taxonomic hierarchy, including different classes of mold such as eurotiomycetes, dothideomycetes, sordariomycetes, zygomycetes and mucormycotina.
Mushrooms
Mushrooms can be more narrowly classified down to the level of their order, which is most often Agaricales. That is, many mushrooms are classified as kingdom: Fungi; phylum: Basidiomycota; subphylum: Agaricomycotina; class: Agaricomycetes; subclass: Agaricomycetidae; and order: Agaricales. The Agaricales order of mushrooms, known as the "gilled mushroom" order, encompasses 33 different families, 413 genera, and more than 13,000 different mushroom species. The identifier "mushroom" has been used for polypores, jelly and coral fungi, and stinkhorns, however, so that the word has come to be associated with fruiting fungal bodies rather than a precise taxonomic classification.