Am I understanding this correctly? All paleo foods are a subset of all primal foods, and all primal foods are a subset of all WAPF foods?
If yes, where does white rice fit? And, I guess all 3 of these are examples of ancestral diets?
As a lover of anything remotely Venn in the diagram universe, I applaud you.
From the "what you can eat" standpoint, you may actually be fairly close to the mark.
However, from a "origin" perspective -
WAPF - Based off the findings and teachings of Weston A. Price and focuses on "Traditional", not necessarily "Ancestral" foods with a more agrarian-bent, prior to the emergence of heavily processed foods (Pre-WW2 era). Think of this, "Paleo is to Caveman as WAPF is to Amish, and you'd have a general idea.
Paleo - Arguments abound as to where "Paleo" really started. Was it Vilhjalmur Stefansson who introduced it, did Loren Cordain actually coin the phrase? All irrelevant. The purpose of Paleo is to initially replicate a pre-agrarian diet by eradicating specific post-agricultural foods such as grains, beans, refined sugars, dairy, and in some circles - tubers (but definitely not the consensus here).
Primal - An iteration of Paleo from Mark Sisson that uses similar logic, but opens the door to some modern foods after some examination (dairy, some legumes with low saponin content, fermented soy). Primal seems to focus primarily on carbs for weightloss, while also retaining much of the logic about antinutrients from the Paleo diet.
Where does white rice fit in? IN those above, nothing. Perfect Health Diet (an example of a "Ancestral Diet" that includes rice) is not a "Paleo" diet per se, instead it is a diet that takes the principles of Paleo and expands it (in similar fashion to the primal diet outlined above) and primarily looks at the content of anti-nutrients in foods.
There is much common ground between all of these. They all exclude refined, processed "foods of technology". They all aim to improve health through un-demonizing foods that were perfectly fine until Ancel Keys and Joseph Kellogg successfully reformed the western world to sick, fat people in the name of notoriety and profit. They also look to our evolutionary (or cultural, in the case of WAPF) past, to provide a healthier future devoid of processed, unnatural food.