機構(n)1:organ;institution
機構(n)2:mechanism
組織(v): organize; form
組織(n):organization; organized system
組織 usually emphasize politics, consciousness, relationship, connection and so on, such as religious organizations, reactionary organizations and so on.
機構 usually emphasize the organization, planning and implementation of the organization. Such as administrative institutions, educational institutions, training institutions, medical institutions and so on.