I hope that I have understood what you wanted to know as you did not actually ask a question. I have tried to guess what you were asking. If this is not what you are asking, please ask another, more detailed question.
The basic difference between these two things is that civil disobedience is a tool that is used to try to get something while civil rights are an end in themselves. Civil rights are the rights that every group of people should enjoy by virtue of being members of a society. The Civil Rights Movement was agitating to have African Americans enjoy the civil rights that white Americans had.
Much of what the movement did was civil disobedience. This is the technique of openly disobeying a law to bring attention to the inequity of that law. African Americans, for example, did things like staging sit-ins at lunch counters where they were not allowed to eat. They were protesting the inequity of laws that allowed such segregation. By openly disobeying the law, they were trying to get it changed.
Thus, civil disobedience is typically used as a tool to get civil rights.