觉得 and 以为 have similar meaning. They both used to express your opinion or feeling about something. But 以为 is only for something that turn out to be not true. For example: 今天我去了他的家，我觉得他的家很大。 Today I went to his house, and I think his house is big. 我以为他的家很大，可是今天我去了以后，我发现很小。 I thought his house is big, but when I went there today, I found it small.

when used to put forward an idea or opinion: 觉得： I think,... ( = 认为， can be followed with your opinion when asked by a question like ： 你怎么看。。。？) 以为： i thought ... ( nowadays more often used in a past tense, especially when someone has said something out of your expectation. For example, 我 还以为 你也去了呢！ 【I thought you went as well! But now you say you didn't!】)

Firstly I would like to say that your question needs fixing to "谁可以帮我了解为什么“觉得”和“以为”不一样？ （帮助 is also ok) 觉得： I think you are in American 我认为你在美国 （When I say the sentence, I 'm not sure whether you are actually in American or not ,but I think you are ) 以为： I thought you were in American ,我以为你在美国 （实际你不在,说话的时候已经知道你不在美国了）... kind of subjunctive mood ，I know you are actually not in Amrican when I say the sentence.

以为，认为，意思差不多，以前也讨论过，不妨自己在网站里找一下。 觉得：有某种感觉或认为，这种认为带有不敢肯定的语气。 认为与觉得，并不是thing与thought之间的区别，汉语不存在时态，也没有什么现在式、过去式之分。你现在认为还是过去认为，还是将来认为，都是认为，没有区别。 我以为，我认为，都在表达自己的主观想法，主观判断，至于对不不对，那是另一个问题。比如： 我一直都以为他家很大，今天去他家了，结果和我以为的一样。 你以为这是真的吗？当然，我就是这么以为的。（当然用成“认为”更多些。） 觉得，表达一个人通过自己的感知之后得出来的不太确定的判断。 我觉得这是真的。你觉得他家很大。 每次听他谈论他家，我一直觉得他家应该很大，结果今天去了之后，一看，也不觉得有多大。

觉得 means feel, and 以为 means thought.