Six-Shooters & Wagons may mechanically play very much like Swords & Wizardry Continual Light but outside of the mechanics it is a completely different style of gaming.
Fantasy is more focused on PC personal gain while Western is more focused on community gain. In SSW your class determines what your character can do mechanically within the game rules but your profession determines who your character is within the world.
Here is a list of professions that your characters could be in SSW:
Marshal (Town or US)
Saloon Worker (Bartender, Piano Player, Owner, etc.)
What role does your character play within the Western game world? Your character's class may be the Gunslinger but their role in the town could be a number of things. Who's to say the Missionary isn't a Gunslinger? Or what about the Mayor of the town is a Vigilante?
Just remember that the class helps define the mechanics but a profession helps defines the character.