When playing through the game as 2B and 9S, you start with their respective default weapons. 2B starts with the Virtuous Contract and 9S starts with the Cruel Oath.
Other than having different descriptions and appearance, both swords seem to be identical. They have had the same stats each time I have upgraded them and it appears it increases both of them have increased attack speeds, as well. Both swords are level 3 in my playthrough with Attack: 420-504, Combo: Lt 6 Hv 3, and ATK Speed Up.
Is there a difference in these swords or is it just lore that distinguishes these 2 swords?