The difference is the atmosphere we use them; 讲（jiang）is a formal word mostly. Eg. When introduing some to give a speech, we will use 欢迎谁讲话（huanying shui jiang hua), but we will never say 欢迎谁说话（huanying shui shuo hua); 说（shuo) is a unformal word, especially in spoken language; somebody say, 谁说（shui shuo)！ Hope this is useful for you!