It is actually the other way around. Prism was just the .NET "flavor" of the Oxygene compiler. Oxygene includes everything that Prism did, plus a whole lot more. Oxygene also includes the Java flavor (for Android development) as well as the soon to be released "Cocoa" edition which is currently code named "Nougat" (for Mac and iOS development).
When Delphi Prism was first released there was some existing .NET resources that were bundled with it, but they deprecated and removed shortly after. Most of the Delphi Prism and Prism releases were solely a subset of Oxygene.
The difference you read in the descriptions comes down to branding. Technically there is none.
In an unrelated note, if you find yourself doing both Oxygene for .NET and Delphi development then you should check out Hydra too.