The other是特指的.Another就是泛指的.
而且the other是两者中的另外一方,而another就是多方之中的一方.
比如说有两个人,一个是学生,一个工人,就可以说：one is a student,and the other is a worker.
如果说三个人,一个是学生,一个是工人,一个是老师,就可以说：one is a student,one is a worker and another one is a teacher.