The PHB defines WIS as following (excerpt):
Wisdom reflects how attuned you are to the world around you and represents perceptiveness and intuition.
and CHA like this:
Charisma measures your ability to interact effectively with others. It includes such factors as confidence and eloquence, and it can represent a charming or commanding personality.
In this question, the accepted answer lists a quote by Mike Mearls stating that CHA is used to save against possession effects.
Another question's answer characterizes WIS saves as:
Resisting effects that charm, frighten, or otherwise assault your willpower
and CHA saves as:
Withstanding effects, such as possession, that would subsume your personality or hurl you to another plane of existence
All of the above match spells (Dominate [x], Command, Suggestion) and abilities (a Ghosts' Possession) from the rulebooks. However, I fail to see why an effect that possesses you and an effect that breaks your willpower, such as a Dominate spell, would use different saving throws. Wouldn't resisting possession also require willpower? Furthermore, the description of the WIS ability score makes no mention of willpower, while CHA mentions a "commanding personality", which is at least similar to willpower.
If it helps, the reason I'm asking is that I'm currently designing a homebrew class themed around possession and resisting it. Intuitively, I wanted to use WIS as the main stat (since high willpower is essential for the class), but now I'm confused, seeing how possession forces CHA instead of WIS saves.
If anyone has a good explanation of how both saves (not so much checks) differ, that would help a lot!