Both of these civil rights movements had several similarities that we can remark upon. However, they are different in many aspects as well.
The civil rights movement in Northern Ireland was mainly a fight for independence and autonomy. Northern Ireland wanted to be free from English rule. They believed their people deserved to enjoy full rights, including that of self-determination. The American civil rights movement was similar in the sense that it wanted to grant Black citizens the opportunity to create their own future. It believed that they deserved to have all the rights that other American citizens have. Moreover, they were both looking for a change in law.
In terms of differences, there are a few we can talk about. The movement in Northern Ireland was against a foreign power, while the civil rights movement was targeting the government of the United States. Moreover, while the movement in Northern Ireland involved all people, the movement in the United States was mostly driven by African Americans.