I agree, it can be confusing and there are more and more amendment products coming out all the time with bacterial and fungal inoculants included as technology and mass production techniques have made them very inexpensive.
Almost all inoculants are delivered in spore form since they can be microencapsulated and kept dormant for long periods of time in a dry or liquid carrier. All fungi reproduce by spores, many bacteria do but not all.
I think it's only accurate to say that bacteria and fungi are ubiquitous in the environment, what beneficial species as well as pathogenic species may be present in native soils will vary with climate, soil type and cultural practices. Cultivated soils for crop production are many times the most abused and damaging to soil life. Excessive tillage, chemical salt fertilizers, fungicides and pesticides can inhibit or kill off many beneficial species including higher forms of life like earthworms, protozoa, beneficial nematodes, mites, and insects that are all important to the
Soil Food Web. Using inoculants are a good way to cheat a little and introduce known species that will be beneficial to the soil and plants faster. Composts help that too.
Your fish tank has is like soil too, it contains bacteria, fungi, algae and other critters also, maybe not all good ones. Being a closed system it takes steps to keep toxins from building up which can kill your fish. Fish waste contains ammonia and nitrites which can get to toxic levels for the fish. Your plants like that fish water in part because those compounds can be converted to ammonium and nitrates by soil bacteria. I found this, there is even a live culture of
Nitrifying Bacteria you can buy that does just that in an aquarium.