认为 comes from thought, inference, reasoning (and sometimes beliefs or trust also).
One says 认为 when he usually has some reason/inference to support his opinion.
相信 only comes from beliefs or trust.
相信 means one trusts something and has no reason/inference but just beliefs or trust.
BTW, 觉得: one has no belief in his opinion and also has no confidence in his reason/inference. That's feel like
.
认为 like think
相信 like believe
觉得 like feel like
想 could be think/believe/guess/want/...
(depended on context), 想 is really wide in usage
我想去吃晚饭 I want to dinner
我想他是对的 I think/believe/guess that he is right (depended on context)
我认为他是对的 I think that he is right (I have reasons/inference)
我相信他 I trust him
我相信他是对的 I believe that he is right (I just trust it and I have no inference)