IIRC the Arcade came about a year after the original X360. I had one of the originals, chrome disc drive and 10GB HD (maybe that was usable space). ... Okay, looked it up and you're right, except it was the 'Core' model. Arcade was two full years after launch.
Difference: Premium cost only $100 more than the Core ($400 vs $300) but came with basically over $200 worth of upgrades incl. HDD, wireless controller, headset, and memory card. You also needed the HDD to play Xbox Live.
Yes, my fault. I actually indeed meant Core and Pro. Totally slipped my mind that Arcade was actually an official edition and had 4GB SSD or something.
Difference: Premium cost only $100 more than the Core ($400 vs $300) but came with basically over $200 worth of upgrades incl. HDD, wireless controller, headset, and memory card. You also needed the HDD to play Xbox Live.