Document Permissions appear different between Reader and Adobe Pro

Yes, in any case Acrobat Reader cannot extract a page.

But indeed, this is more of a functionality restriction than an editing restriction.

I assume that you mean the information in the lower half of the second tab ("Security") of the document properties.

This lower half has the title "Document Restrictions Summary". And in this summary not only aspects of the document itself are summarized but also aspects of the PDF processor! For example, Acrobat Reader simply does not by default offer some features to the user, and these restrictions also are represented in the "Document Restrictions Summary".

For some more details read this and this stack overflow answer.