Encyclopedia of Life's Definition:
All mushrooms are fungi, but not all fungi are mushrooms. For those fungi that produce them, the mushroom plays a similar role to a flower or a fruit in plants. Some part of each mature mushroom produces microscopic spores that are similar to pollen or seeds, sometimes numbering in the trillions . The rest of the fungal organism typically lives in the soil, wood, or some other material and is composed of thread-like strands known as mycelium. The expanding growth of the mycelium often results in circles of mushrooms or “fairy rings.” An individual mycelium can grow quite large, with at least one well-documented case covering more than 1,500 acres in Oregon .
Many mushroom-producing species are important decomposers, particularly of wood. These species are often relatively easy to cultivate. However, many species have a special, symbiotic, “mycorrhizal” relationship with particular species of plants. Often, neither the mushroom nor the plant will grow without a mycorrhizal partner.
Most mushroom-producing fungi are members of the phylums Basidiomycota or Ascomycota. The technical difference between these groups has to do with how the spores develop, which can be detected only by using a microscope. However, the “ascos” (ascospores) are less frequently noticed and are often shaped like small cups. Probably the best-known ascos are the highly prized morels (genus Morchella), which typically fruit in the spring and are often mycorrhizal, or the true truffles (genus Tuber), all of which are mycorrhizal.
Wilson, Nathan. 2018. "What is a Mushroom". Accessed 08 Feb 2018, Available from Encyclopedia of Life, http://www.http://eol.org/info/453.