It's true that in 5th ed, most Abilities are very "grainy" - one skill for all one-handed weapons, one skill to ride anything, one skill for any athletic effort, another for all things legal, and one that lets you play any instrument. But it's also true that, especially in medieval times, a craft or profession was a very narrow field of endeavour. There were grain merchants for mills, grain merchants for people, and grain merchants for horses; hay merchants for horses, and hay merchants for thatching, and hay merchants for human bedding - and so on.
Smithing is especially tough, because even today we know that iron and silver and gold have very different crafting properties, as well as having the traditional distinctions mentioned above.
Technically, a blacksmith and a weaponsmith are not on the same scale of "smiths" - "black" refers to iron and iron only, and "weapon"... yeah, so you could have a blackmith who specializes in weapons and literally be a weaponsmith without a problem. Most smiths were skilled in a single type of metal, rather than a single type of final product, but with weapons, armour and some other high-end products, a variety of crafts were combined toward that final compound product - a metal, some leather, some wood, whatever. But it would be the rare "Craft: Weaponsmith" that would allow one to forge an iron axe, a damascus steel scimitar, a silver arrowhead, a golden dagger and a bronze shortsword. (Maybe beyond rare.)
However - this is AM, and a role playing game, not as such it's a rough approximation and not a simulation of RL. The goal is a good story and "fun". So, maybe "swordsmith" was seen by that Story Guide as being a reasonable, appropriately- and tightly-defined field of pursuit, balanced for their saga and their players.
Instead, one could just as easily draw a distinction between a "smith", who makes purely functional items, and an "artistic metal smith", who might work any metal to a different end, and a "weapon smith" who rolls that way. They all could work iron or bronze or silver (which all have different properties), but one would be making functional items, the other artistic ones and the last weapons.
And other distinctions would work as well, or better for a diff saga. Maybe even as broad as "smith".
The Abilities are grainy, so maybe better if you err on the side of generosity. And tossing the players a cookie is not always a bad thing.