Although many people use them interchangeably, there is a slight difference in my opinion.
"Believe" is something you trust to be true and you place your faith and trust in it. This is a personal value and has a more personal element in it.
"Think" can indicate a mental process at work, and it indicates an opinion of yours or some facts that you have gathered.
"Do you believe in the presence of extraterrestrial being?" asked Zoe.
Tom answered, "Yes, I believe so."
"Is there a solution to this problem?" asked the manager.
"I think so, it is on page 25 of the manual."
Back to your second question,
Then, can I say "I believe that she is wise." instead of "I think that she is wise."?
Yes, as you place your trust that she has wisdom.
So, my answer to your question is : Yes, I THINK so.
Hope this helps.