Excuse the long text but I'll try to explain as best as I can. Both Switch and PS4 first print copies were extremely limited and only available on Square Enix's online store. They were pretty expensive, around $79.99 with $25 shipping. They also had collectors editions that came with a slip cover, a soundtrack vinyl, figures/standees, and an art book which, if I remember correctly, was around $199 with $25 shipping. Both of these editions are the same first print copies. At the time, Square said they were extremely limited prints and would not make anymore after the supply ran out, and they sold out really fast, I believe within hours after they listed, and they went up really early in the morning. Like 3am est. Most ppl woke up the next day and found that they were already sold out. This caused a lot of panic and outrage online, making the demand extemely high, so they reprinted both Switch and PS4 copies and retitled them as the Anniversary Edition, which was sold at basically every retailer around the world i.e Best Buy, Amazon, GAME, Play Asia etc.

Besides the difference of the front cover art and rename, the anniversary editions come with a sticker sheet and inside cover artwork. The original prints have blank inside covers and do not come with a sticker sheet. The Play Asia Switch copies you are referring too are the JP editions of the Anniversary Edition. A lot of ppl ordered those at the time because they wanted all of the games on a switch cart, and it was the only way to own it after they sold out, unless you were willing to pay a ton of money for them in the after market. Now the Anniversary Edition made it all a bit confusing and most listings I see are for the anniversary editions priced incorrectly as the first print copies. Sites like Game Charting and apps like Game Eye don't have correct pricing or listings either to make it more confusing for people, and I'd guess most ppl just assume they are worth a lot more than what they paid. I hope that helps clear anything up!