I am not clear on the difference between TTL auto operation and P-TTL auto flash operation on the new digital cameras.

What is the difference, and what are the limitations?

On film cameras TTL (Through The Lens) metering was a way for the camera/flash to measure the actual exposure and respond accordingly.

With digital there have been variants of that (D-TTL, I-TTL - both Nikon) that have refined the basic TTL idea and do essentially the same thing, but in a more refined way. Canon, I believe, also have a TTL variant.

I have not heard of P-TTL specifically, but I suspect it is a manufacturer's specific implementation of TTL for use with their cameras.