Shedding is the process of losing hair, when the hair follicle dies, the hair falls out of the animal's skin.
Molting is the process of running out of room to grow, whether it's because old skin has become too tight, an exoskeleton too small, or feathers have become damaged.
To be clear, there is more to the process of molting than the end part where the old skin, shell, or feathers are left behind. For animals that can regrow limbs, they do it through the process of molting, and I think it would be extremely confusing why a question asking about whether or not a tarantula will regrow a fang in their next molt would be tagged with shedding.
I know people tend to call it shedding when talking about reptiles (I do too sometimes), but the process is molting, and I don't think it's fair to people who own invertebrates or birds to suddenly lump their molting questions into the shedding tag just because it sometimes gets called shedding for reptiles.
I also think it's more valuable to be technically correct when it comes to tags than simply using what terms people call things. That's why fish-tank will send people to aquarium and cavy will send people to guinea-pigs.
Since we can't really create a synonym either way, I think it's best if we manually fix the tags as questions come in (mammals with shedding others with molting). There aren't too many questions on either subject, and it will keep away any confusion as to why we're saying that invertebrates and birds shed.
If anything, I think it makes more sense to have shedding as a synonym of molting, since animals shedding fur as the season change is technically a form of molting.