On a lower level one could argue different weapons have different properties. A different size, different weighting and so on. That's especially true for weapons that are individually crafted for one customer.
The average swordsman wouldn't notice this. For him a sword isn't the primary weapon anyways, as I wrote above. But a master fighter will. He fights better with his own weapon that the smith matched especially for him, than with any other sword. Maybe that's what the duelists talk about when they talk about the personality or character of a sword.
And then, depending on the world, it could be that things that are used with dedication over a period of time awaken in some sort. I think the Japanese have a believe system where old items get some awareness over time. There it needs centuries, but you could shorten that in your world.
The average swordsman wouldn't notice this. For him a sword isn't the primary weapon anyways, as I wrote above. But a master fighter will. He fights better with his own weapon that the smith matched especially for him, than with any other sword. Maybe that's what the duelists talk about when they talk about the personality or character of a sword.
And then, depending on the world, it could be that things that are used with dedication over a period of time awaken in some sort. I think the Japanese have a believe system where old items get some awareness over time. There it needs centuries, but you could shorten that in your world.