That is how they are depicted in Takhteh Jamsheed (aka Persepolis). In the first pic from the OP, you will note Persian soldiers have the flutted hats, and the

That is how they are depicted in Takhteh Jamsheed (aka Persepolis). In the first pic from the OP, you will note Persian soldiers have the flutted hats, and the Medes have the round hat. Apadanah depicts the procession of Nations that presented themselves at Spring Soltice (Persian NoRouz literally "New Day") to the court, in their national garb: https://media.gettyimages.com/photos/apadana-in-persepolis-procession-of-the-delegations-of-the-vassal-of-picture-id640265343?s=2048x2048 https://media.gettyimages.com/photos/apadana-in-persepolis-p...