Powdery Mildew is a fast-spreading fungal disease. It is one of the most common and recognisable problems in a garden but doesn't cause significant damage to plants. Unlike other fungal diseases, powdery mildew does not require moisture to infect a plant and is mostly associated with water stress of plants (due to unusually high water content in the spores of the fungi).
There are many different species of powdery mildew, and these species tend to have a narrow host range allowing them to infect very few species. This tends to mean that if an apple tree had an infection that it could not transmit it to an oak tree, but it is possible for some plants to be infected with multiple species of powdery mildew at the same time.