What is the difference between "current user" and "current page user"?

Well, you can do that with some caveats. I wrote up a description of a potential way to do this in another thread. (See the thread for context.) This started as a discussion of domain forwarding but then turned into a question about whether one could do “LinkedIn” style profile page URLs. In this post reply, I detail one approach (which is more-or-less the approach available, if you generalize it):

Hope this helps.