If the anvil has two recipes with the same input, but a different tool produces a different output, only one of them works. For example, pickaxing an ingot results in a shard, if we also add a recipe to hammer ingots into plates, that recipe will show up in JEI, but not actually work in-game, since AnvilRecipe.getRecipe(ItemStack input, EnumTier tier) only returns one recipe.

I was going to report this as a bug, but it seems like it's quite fundamental to how anvils function, so it's probably more of a request.