When I try translating these two words into Chinese, I find they have the same meaning in Chinese. But how do natives use the two words?
An opinion is something that is a personal belief, and perhaps not universally accepted. A good example of this would be the Opinion column of a newspaper, where the editor discusses a position on an issue with more emotion and personal perspective than the rest of the fact-checked and neutral paper. By marking this column as "Opinion", the editor makes it distinct from the News, and the reader is expected to understand that the Editor is speaking only for themselves.
Since an opinion does not need to have the weight of evidence behind it, it is also used as a way to dismiss someone's position: https://www.youtube.com/watch?v=pWdd6_ZxX8c
A concept means an idea, and comes from the same word as "conception", meaning the point at which something new is created.
One example might be "concept" cars, exotic and elaborate vehicle designs that are never intended for mass production, but exist as showcases for art and engineering. http://en.wikipedia.org/wiki/Concept_car
A concept can be an opinion when regarded as an abstract idea or a general judgement but an opinion is only something abstract that you can not feel. You can only perceive it in your mind.
Conversely, a concept may have a concrete meaning, it can be a construct, a theory, a design, that is something palpable. See definition #3 and #4 of Collins English Dictionary.