Here are the differences that I have gathered so far:
AP has diagonal back braces, P does not.
AP has side braces, P does not.
AP is available on:
600 (Maple)
800 (Rosewood)
900 (Rosewood)
2014 Fall Limited 700 (Sassafrass)
2015 Guitar Center custom 500s (Quilted Mahogany and Blackwood).
P is available on:
500 (Mahogany)
2016 Spring Limited 400 (Rosewood)
If you have any further information, please feel free to share!