Church vs. church: a church (lowercase) is the place we worship, like St. Luke. The ‘Church’ encompasses every Catholic in the world, now over 1 Billion people.
Our Church is ‘apostolic’ meaning that the Jesus laid hands upon the apostles that began his ministry. The apostle St Paul laid hands on his successor and that man laid hands on the next. This happens over and over until the current apostolic succession of Pope Benedict XVI to Pope Francis. The entire 2,000 year history of succession is recorded in Church histories.
The Pope leads our Church with support of over 200 Cardinals and under them, many Archbishops. Bishops report to Archbishops. The Pope guides from the Vatican. Archbishops run each Archdiocese, containing several (3-10) Dioceses which are headed by a Bishop(s). Within each Diocese there are many Parishes, like St. Luke, run by a Pastor. Other priests serve in every level of the organization with over 1,000,000 priests in the world.
‘St. Luke Parish’ is part of the ‘Diocese of Phoenix’ within the ‘Archdiocese of Santa Fe’. Father Pawel works for Bishop Olmsed and Aux. Bishop Nevares. Our Bishops report to Archbishop John Charles Wester.