相信 is belief that one holds to be correct and have no doubts about. 我相信他肯定遇到意外事件了，否则他会按时到的。I believe he must have had an accident, otherwise he would have arrived on time. 认为 is to hold or formed an opinion toward a particular person or thing; 有些人似乎认为这种挫败是要无可避免的。Some people think this defeat will be inevitably so 相信 is a type of 认为

认为 = in my opinion 相信 = to believe/belief

Generally, 相信 is followed by a conclusion that you think that is right or strongly believe. 1. 我相信你说的话。 I believe what you said (is true). (i'm confident in you)(can lead a Noun. structure) 2. 我相信你会拿到冠军的。 I believe that you'll get the title of the champion. (strongly believe) 3. 我相信地球上有外星人。 I believe that there are aliens on the Earth. (strongly think sth. is true) And 认为 is equivalent to think, followed by a complete or partly thought or opinion. 1. 我认为你说的是对的。 I think what you've said is true. ( anyway, 认为 should be followed by a complete sentence) 2. 我认为这道题应该选A。 I think for this question A is the right answer. (just a normal opinion ) 3. 我认为地球上有外星人。 I think there're aliens on the Earth. (just my opinion, compared to 相信有, the speaker is less of confidence) Hope this helps.

Usually Chinese people translate "I think" as 我 认为 , and "I believe" as "我 相信”. So can you tell me here the difference between "think" and "believe"? In my understanding, behind the saying of “我认为...”, there is a reason while “我相信” is just "trust". Like 'believe' is related to 'belief', "相信’ is related to '信任（trust）or 信仰（belief) which has no reason.

Well, I would say you are right about the translation! I believe you. 我相信你 Here believe is translated as 相信, believe someone, is translated as 相信. I believe in miracles. 我相信奇迹 I think believe in is always translated as 相信, no matter what you are believing in. As for 认为, I believe that we will win. 我认为我们会赢. Here is a bit confusing, you can translate believe as 相信, to me, which adds the feeling that we will definitely 100% win! If you translate it as 认为, I feels that we might lose, but most likely we are gonna win, but there is an uncertainty. To me, 相信 is more certain than 认为.