Most of what you read online is incorrect, then, or at least misleading. Willpower isn’t actually a stat in D&D. When your character asserts their will, they succeed at doing so, full stop. The save is for whether or not the character has an opportunity to do so.
What you have instead are Intelligence, Wisdom, and Charisma.
Intelligence saves are how much your character knows. An example here is illusion magic. Illusions are imperfect, and better understanding of nuance lets a character see an illusion as false, and then exert their will to disregard it.
Wisdom saves are about how much you can perceive and intuit. When someone attempts to control you, it’s subtle, and the saving throw is about noticing that something is wrong. Once you notice it, your character exerts their will and shrugs it off.
Charisma saves are about your force of personality and sense of identity. When someone attempts to possess your body, they are attempting to change who you are, and is directly opposed by how strongly you believe in yourself, and how strongly you believe in who you are. Once you resist the attempt, you then exert your will and drive the spirit out.