Straight swords stab better, curved swords slash better, armor makes slashing ineffective and the further west you got the stronger the armour you found, so straight swords.

After a while armour got so good that penetration of the metal itself became impossible, so you needed to aim for gaps and weak points, hence the rise of long thin straight blades.

Then armour got btfo by guns, bullet proofing required armor so thick you couldnt proof the entire body without becoming immobile, so you get a transition of less and less coverage meaning, hey, curves swords are usefull again!

Out comes curved western sabers, and bullets just keep getting better so eventually noone bothers with armor save for status symbols and dedicated melee cavalry.

I got the reference