As always, Hilary's answer is clear and accurate.
We use "I wish...would" when we'd like something to happen, as in Hilary's examples : "I wish it would stop raining" or "I wish he would stop yelling". These are things which will inevitably happen at some point; your wish is for them to happen very soon.
In other cases, we use "I wish ...would" to express dissatisfaction about a habit or situation which could easily change or which is within someone's power to change. For example, "I wish you wouldn't talk about your ex-wife/ ex-husband so much". As Hilary says, this is about volition. You know that the other person is capable of altering their behaviour, and you are basically asking them to make this change. This is something which you want to happen.
This is different from saying "It's such a shame that the Coronavirus lockdown means we can't celebrate Grandma's 80th birthday today. I really wish we could all be together". This is how we would like things to be. In this situation, we are taking about something which we cannot change. We feel regret that this is how the situation is and we are expressing a desire for it to be otherwise. However, this desired situation is entirely hypothetical: we would like things to be different but we know that this is not possible.
Compare these two statements:
"I wish you would help me" =
"Please help me !". You are able to help me but you don't seem willing to do so. I'm trying to persuade you to change your mind. I know that this situation can change. This is something I want to happen.
"I wish you could help me" =
"Never mind!". I know that you can't help me, and I'm saying that this is a shame. You're expressing a desire for how you would like things to be, although you know that this is not possible.
I hope that helps.