Well, in my own opinion, Physical Address Extension reflects two things, Physical-Address Extension and the way to implement the extension of physical addressing when the architecture stays unchanged. The phrase your mentioned here only embraces the former but omits the most important thing which the original one has already embraced.
Enhanced Version of PAE
For months, I've also noticed this discussion happened on both Intel and AMD forum. Frankly, I would deny this suppose. The paging in AMD64 architecture is not an enhanced version of PAE, but just based on it. We could not call it as an Enhanced Version of PAE, Physical Address Extension! AMD64 is a standalone 64-bit architecture, mainly invented by AMD, and later incorporated into x86 family. Intel also made their ISA-level compatible processors, but they call their products as Intel64, not AMD64. When processor working under its native mode, 64-bit mode of both AMD64 and Intel64 processors, the virtual address is directly mapping into their corresponding physical-address format. There is nothing used to extend both address and address method. So we could not make that conclusion. PAE only happens to IA-32 processor with PAE-enabled or AMD64/Intel64 processors when working under legacy mode (non-native mode)!
I need your help badly! The above words I said on Wikipedia, Talk:Physical Address Extension - Wikipedia, the free encyclopedia, but removed, removed and removed! Is there anything wrong with it? I have already wasted my energies and times for years to dealing with those so-called professionals there, I want to that Item, PAE, on wiki won't mislead innocent readers too a lot! So I need your help! Maybe I am wrong, but at least, this is my kindest struggle that I made!