First off, NaCl (salt) is salt.
Aquarium salt, is no different than the salt you put in your water softener, or on your side walk, or on your food, only the cost is different.
To really cure ich, the salinity of the water in your tank needs to be equal to, or exceed 3ppt (parts per thousand).
I put rock salt in my tanks until the salinity meter exceeds 3ppt (by the way, the salinity of the ocean is @ 35ppt).
And to cure ich, it has to run its reproductive cycle, and will take at least a few weeks.
Just because the spots leave the fish, doesn't mean all the ice parasites are gone, some may be dormant, and will hatch out. Heat speeds the reproductive cycle, and gives the salt a chance to work, the salt kills newly emerging ich, it does not kill the ones on the body of the fish, it kills them as they hatch off the fishes body.
The fuzzy growth, could be a secondary infection, that attacks the lesions on the fish body, where newly hatched parasites came out.