Oh yes, they definitely have different uniforms!
Though most fighters in the military will be average joe soldiers, so they won't really get special uniforms. Back in the day, soldiers had to be rather wealthy to afford their own armor, and much of it was hand-me-downs if they were lucky! Most soldiers have to supply their own equipment, so there's no real standard uniform until you get higher up in rank. So knights and generals and officers will definitely have uniforms, but a regular guy drafted into service? Not so much.
I'll have to talk to Tally for more info and brainstorming about what sorts of different uniforms the nations might have! Because they will all be different styles from nation to nation.