Thrush can be caused by fungus, bacteria, or yeast. Rain rot is most often caused by bacteria, with only very few cases caused by an actual fungus.
I use the same product on both, apple cider vinegar, straight up. It kills bacteria, changes the PH to make yeast die out, and kills fungus. I get the cheap ACV from wal-mart, $3.78 a bottle. Put some in a spray bottle and spray feet 2-3 times a week to prevent thrush, daily to get rid of it. Spray rain rot daily, pick off scabs, and dunk grooming tools in a 10% bleach solution after every use.
I also feed my horses 1/2 cup of ACV daily, mixed in their feed. It works to prevent rain rot and encourage drinking. It also keeps the "boys" cleaner.