Final answer:
The first type of church organization is the ecclesia, which is a dominant religious institution often recognized as the official religion. The second type is the denomination, which is a mainstream organization that does not claim official status.
Step-by-step explanation:
The first type of church organization is the ecclesia, which refers to a dominant religious organization that includes most members of society and is recognized as the national or official religion. An example of this is the Church of England. The second type of church organization is the denomination, which is a large, mainstream religious organization, but it does not claim to be the state's official religion. Denominations coexist with other religious groups and typically tolerate the presence of other faiths, endorsing a particular creed, form of worship, or organizational structure.
Different religious organizations may also be referred to as sects, which are smaller and often considered to break away from larger denominational or ecclesiastical institutions, and cults, which are religious groups that are often small, secretive, and may have practices considered unorthodox or deviant.