Gill Fungi
Many of the mushrooms sold in grocery stores, as well as some of the deadly poisonous varieties, fall under the broad category of gill fungi. These mushrooms are commonly characterized by a cap, stalk and long thin blades of fungal material, called gills that form on the bottom side of the cap. Puffballs, which don't form a cap and stalk, are similar to the gill mushrooms.
Fungi With Pores
Multi-cellular fungi are similar to the gill mushrooms. This group of fungi produces a porous surface that makes spores. It contains the shelf fungi that infect dead or dying trees, as well as the pore fungi, which form a cap and stalk but still lack gills on the underside. Instead, a vast comb-like structure forms beneath the cap. In either case, the pores form on the underside of the main structure of the mushroom and are released into the environment during reproduction.
Sac Fungi
Sac fungi are another grouping of fungi that vary widely in size. Single-celled yeast units are included in this grouping, as are morels and truffles -- two types of large multi-cellular life forms that are prized by gourmet mushroom hunters in many parts of the world. Also found within this group is the wheat ergot, a plant pathogen, whose byproduct is commonly known as LSD. Sac fungi sexually reproduce from the creation of an embryonic cell called an ascus. Many of the fungi, which grow with algae to form lichens, are also part of the Asomycetes or sac fungi grouping.
Molds
Black bread molds and most molds create another grouping of fungi that primarily live in a terrestrial environment and decompose the remains of plants and animals. These fungi are known as Zygospores and reproduce sexually, even though there is no distinguishable male and female parts.
Miscellaneous
These four groups do not define every type of fungi. Leftover are a variety of fungi types that fail to fit in the above groups. In general, this grouping consists of small, asexual fungal units that grow in mass to create diseases such as athlete's foot or ringworm. Also included are the organisms that help make Roquefort and Camembert cheeses or produce penicillin.