All mushrooms are fungi, but not all fungi are mushrooms. Indeed, the fundamental difference between mushrooms and fungi is that the mushrooms are fruiting bodies of specific fungi that are part of the order Agaricales of phylum Basidiomycota. In contrast, a fungus is any member of the eukaryotic microorganisms, such as yeast, molds, mildews, mushrooms, etc., that belong to the kingdom of Fungi.

Though we consider mushrooms a vegetable, they are not actual plants. Gardeners may think of fungus as an organism that's all roots, occasional flowers (mushrooms), and has no leaves, even though part of the mature mushroom produces microscopic spores similar to pollen or seed.

Since mushrooms have no chlorophyll and cannot produce energy from the sun as plants do, they must live off other plants and plant matter, like compost organic matter. The rest of the fungal organism usually lives in the soil, wood, or some other material and is composed of tread – like strands known as mycelium.
Below the mushrooms are minuscule roots-like networks called hyphae. Some cling to plant roots, creating strands that reach far into the soil, increasing the surface area of plant roots.

According to Master Gardeners, “the key difference between hyphae and mycelium is that hyphae are long branching thread-like structures of multicellular fungi while mycelium is a collection of hyphae which makes the fungus.” Moreover, many mushroom species have a unique, symbiotic, “mycorrhizal” relationship with particular species of plants and serve as a secondary root system, spreading far into the soil to extract water and minerals for the host plant. In return, the plant supplies sugars to the fungi to live. These relationships between hyphae and roots working together are called mycorrhizae. Usually, neither the mushroom nor the plants will grow without a “mycorrhizal” partner. So, mushrooms produced by these fungi are akin to flowers or fruit to plants in our yards.

Experts indicate that mushrooms may go undetected for months until the right growing conditions are present for them to sprout. They are not signs of wet soil but will develop when the soil moisture is suitable. Fungi, slime molds, and beneficial bacteria are workhorses for our soils. They indicate healthy soils for trees and other plants to grow in, and they do not cause harm to the garden. Additionally, the mycorrhizal filaments of fungi generate organic compounds that bond soils together, increase their structure and permeability, move nutrients around, and work with other soil organisms to improve root growth. Furthermore, mycorrhizal in the soil has been shown to suppress soil-borne pathogens and protect plants from root diseases.

“Overwatering, over-fertilization, and fungicides can eliminate mycorrhizae usefulness or kill the fungi.” Despite their benefits to soil and plants, gardeners might want to remove mushrooms from their yards if they are worried that they could be poisonous and harmful to children and pets. Rake them and bury them in the compost pile. After a while, mushrooms will stop sprouting, and the mass of hyphae will live unobtrusively for another year. When you see a mushroom in your garden, consider it a sign of a happy mini ecosystem.

The swelling growth of the mycelium often results in circles of mushrooms or “fairy rings.” Fairy rings are subjects of much folklore and myth. The most popular belief is that at night little fairies will dance the night away in the circle, resting on toadstool “chairs” between dances.

In brief, soil fungi, slime molds, and bacteria are a natural part of our gardens. They provide soil biology, soil chemistry, and plant and human nutrition.

https://extension.oregonstate.edu/news/mushrooms-can-mean-healthy-soil
https://ucanr.edu/blogs/blogcore/postdetail.cfm?postnum=51404
https://wattersgardencenter.com/mushrooms-friends-or-foes-to-lawn-and-garden/
https://s3.wp.wsu.edu/uploads/sites/403/2015/03/mycorrhizae.pdf
https://www.differencebetween.com/difference-between-mushrooms-and-vs-fungus/