No, not every fungal growth which you see will be armillaria sp.
I use a lot of compost and manure due to the low-fertility of my soil and I get all kinds of fungi (including proper mushrooms!) appearing after periods of rain; they're just doing what fungi do; breaking-down dead plant material.
There are, indeed, many different types of fungus - and many of them love to grow on dead plant roots in particular, but also dead stems. Most are normal and not doing any particular harm to healthy plants. Plants which are sickly are far more likely to become infected than those which are healthy. Even armillaria honey fungus much prefers dead or sickly plant material. It has a reputation for killing trees, but it is my belief that in many cases the tree was not fully healthy (or was nutrient-deficient, or overcrowded by other trees) in the first place and therefore more easily affected.
Plants lacking in potassium, phosphorus or trace elements are less able to resist disease.
"Fish blood and bone" fertiliser is a good non-synthetic mix of nutrients and I use small amounts along with well-rotted manure.
I was under the impression that honey fungus (armillaria sp) would produce black fungal strands both in the soil and under the bark of dying trees. You are speaking of white growth, which sounds like a different type of fungus.
There are apparently several sub-species of armillaria of varying destructiveness.
I suggest putting up some pictures of the fungal strands and any mushroom-like fruiting bodies which are being produced. The appearance is usually distinctive.
For now, I would be alert and cautious, but certainly not panicking.