Student or Learner
Is there any difference in the meaning between 2 sentences?
1. I think it's going to rain.
2. It looks like it's going to rain.
I'm trying to understand what you're asking. The sentences both have "it's going to rain." which in your example, in my opinion, does not affect the difference in meaning. Therefore, the difference between the two is simply 1. means it's your opinion or belief, while 2. means there is visual evidence. There is no subtlety here.
Here is an example where I think the meanings are not different, or at least very close.
1. I think we're in trouble.
2. It looks like we're in trouble.