Difference between fungus and thrush: If you swipe a hoofpick deep into fungus-infected tissue, it will smell "cheesy" like a yeast (Candida) infection. The back half of the frog peels off in deep layers, and the frog never becomes a wide, healthy triangle. The diseased tissue is light gray to white in color, or black between the peeling layers; healthy frog is medium gray.
By comparison, thrush has a nasty, rotten smell, the tissue is black and slimy, and it tends to begin in the collateral grooves. Thrush is another wet-season problem. In wet areas, people use Kopertox daily in the grooves of their horses' feet but it is a nasty poison, both for us and the horses, and in the environment. "Thrush-buster," which contains Gentian Violet, is also effective and is not poisonous.
"White line disease" is probably a form of fungus. There will be an area where tapping on the hoof wall makes a hollow sound. However, I think most of what people are calling "white line disease" is, instead, a very stretched white line; stretched white line tissue does look strange. Among several hundred horses I have trimmed, I have yet to see a true case of "white line disease."
Fungus is not thrush and must be treated differently. Treating for thrush (Kopertox, Thrush Buster, etc.) will make the fungus worse, because the fungus feeds on the dead thrush cells.