Craft is what you use to make goods; you can make goods and sell them.
Profession is what you use to hold down a job, or run a business; you can get paid by employer or customer.
A blacksmith, obviously, is a bit of both—you have to run your business, but you also have to actually make the items.
And complicating matters somewhat further, there is no Craft (blacksmithing); there’s Craft (weaponsmithing) and Craft (armorsmithing), where you can make weapons or armor from any material, but you can’t use any of those materials to make anything else. This kind of makes sense—weapons and armor must be made very carefully, at least they’re to be much good, and there’s definitely a fair amount of skills that don’t overlap. But you still need to know how to work materials, and if you know how to work materials, you should be able to do other basic stuff with them. To wit, there’s no way someone capable of making a masterwork longsword is going to be unable to make a horseshoe.
Which kind of gets to the heart of the problem: the reason things are the way they are is because Pathfinder gets these rules from Dungeons & Dragons, and Dungeons & Dragons is a game devoted to delving dungeons and slaying dragons. Weapons and armor are items of interest; horseshoes, largely, are not.
Running a business, likewise, is not really the focus of Pathfinder. It’s a really terrible system for that purpose, with overly-simplified, easily-abused rules for the economy. The Kingmaker adventure has somewhat more detail, but they don’t stand up to much scrutiny either.
Which is why Wizards of the Coast explicitly recommended against putting ranks in, say, Profession, because your character has a background as a blacksmith. Even if he ran his own forge and arguably would need that skill, it isn’t relevant to the adventure. His skills crafting weapons and/or armor, those are relevant to the adventure. Profession, in short, was never more than a background detail, for NPCs. In later books, they all but acknowledge outright that it was a mistake to include at all.
Pathfinder’s answer to this issue was, instead, “background skills,” which were skills you could get ranks in without spending your actual skill points. Profession is one of them. I like this answer less well, simply because it’s a band-aid over a mistake rather than admitting that a mistake was made in the first place, but it works well enough. Even among background skills, though, Profession is an extremely poor choice—you still get a limited number of background skill points, and while they can’t be used for anything particularly good, Profession goes unused in almost all games of Pathfinder—even background skills can be better than nothing.
Which is all a long way of saying that, if your character is a blacksmith, ranks in Craft (weaponsmithing) and/or Craft (armorsmithing) is appropriate. Ranks in Profession are not.