Princess Luna and Princess Celestia getting coronated as Equestria's first Princesses. Luna the Princess of the Moon and Celestia the Princess Of The Sun. Because they're very new, they don't have their advanced magic yet, hence the reason they look different.

And no, this isn't canon, this is my interpetation and…I was inspired by actual coronations in Europe, so Celestia has the Scepter and Orb that the Sovereign would hold and Luna has the two Scepters that the Sovereign Consort holds. Although both are Sovereigns, Luna is the younger sister so her rank is lower than Celestia, possibly the reason why Luna rules the night, while Celestia rules technically both, but doesn't take care of the moon or tend to ponies' dreams. And also, the outfits are based off of the robes they wear during Twilight's coronation as a Princess.