Yes, in general, mushrooms are the fruiting bodies of basidiomycetes fungi. Most mycorrhiza are basidiomycetes, though there are some ascomycetes mycorrhiza. In any given location in North America the soil in the ground will have 5 to 25 species of mycorrhiza fungi, some places like old growth forests will have much higher diversity, in some farm fields where chemicals are used, diversity might be lower. Average city backyard might be 5 to 25 species. If I am remembering my Paul Staments correctly.
In a bonsai pot, the diversity tends to be lower, and there can be a regular die off of mycorrhiza and replacement of mycorrhiza, especially if you use chemical fertilizers. . The spores are everywhere in the air, so if a dose of liquid chemical fertilizer is hot enough to kill off mycorrhiza, new spore land and begin recolonizing the pot within days.
Mycorrhizal fungi often have really small mushrooms, very dainty. They only appear during episodes of high humidity and will be above the soil for only a few hours. They "melt" away in the first low humidity breeze. I see them most often in late summer, but you can see them any time of year.
If you are a mycophile, make a spore print. Also photograph, (need a good macro lens) the gill pattern on the underside of the cap. Armed with close up photos, and a spore print, you might be able to key out which genus and maybe which species of fungi you have. More than half North American species of mushrooms are as of yet undescribed. Keys will get you to related European genus, then leave you scratching your head..
If you ever want to describe a new species, get into fungi taxonomy, there is a world of "new things" waiting to be looked at closely.
