Are you getting prime video or Amazon prime? Because they're not the same. Prime video is the streaming service and Amazon prime gives you free shipping, Amazon music, Amazon photos, kindle and prime video. You can get prime video by itself without having Amazon prime. Also you mean subscribe not buy. More on reddit.com

Prime is different from Netflix/Hulu/etc in that it is also a retailer. “Available on Prime” means you can get the title on Prime. That can be renting or buying the title. “Included with Prime” means it is available as a part of the Prime Video streaming subscription content. It’s confusing, and I think the inclusion of all the channels (and the splintering of the service into reg Prime v FreeVee) makes it even more so. I use JustWatch and try to recommend it as much as I can. You can search titles to see what included on any of your steaming platforms. For Prime, it differentiates between what you have to rent/buy vs. what is included as a part of a Prime Video streaming subscription. It’s very helpful imo. More on reddit.com

Premium subscription means it's not on Prime, but it's on a network that you can subscribe to through Prime. In the case above, it's on HBO Max, but you can subscribe to Max independently or through Amazon, Youtube, or Hulu. More on reddit.com

It still exists. https://www.businessinsider.com/guides/streaming/what-is-prime-video The service is available as part of a full Amazon Prime membership for $15/month or as a stand-alone plan for $9/month. Ad-free streaming costs an extra $3/month. More on reddit.com