It could rain later.
It might rain later.
The difference is expressed very well by the quote below, from post #19:
"Could" means it's not objectively impossible; "might" means you think there's a reasonable chance it will happen.
Personally, I don't think it makes much sense to say that one or the other sentences expresses 'stronger' possibility. I see them as
different kinds of possibility. The important difference between the two sentences above is that
only the second is clearly a prediction. That is why
might is the best answer in a scenario where somebody advises taking an umbrella.
Although the second sentence could be used as a prediction, it isn't really good for that. We use
could as a way of saying what is very generally possible. Look:
A meteor could fall out of the sky and land on your head.
I'm not making a prediction here, I'm just saying that this eventuality is not technically impossible. You can read it as a
hypothetical possibility. If you say this sentence to me, I would respond by saying "Yes, true." Now compare this:
A meteor might fall out of the sky and land on your head.
Now you're presenting this outcome as a
real possibility. If you say this sentence to me, I would respond by saying "Don't be silly."