In this context they mean the same thing. This is because "I think that" (note the word "that") means the same thing as, "I believe." However "think" and "believe" do not quite mean the same thing. You can "think about" something - meaning you consider it - but you cannot "believe about" something. In short to think means to consider, to believe means to think something is true.

Perhaps you don't need a reason to believe. It's more like a feeling.