The former were under a regular discipline and subordination to the papal authority.
前者受到教皇权威的正规纪律和服从。
英语百科
Primacy of the Bishop of Rome
(重定向自Papal Authority)
The primacy of the Bishop of Rome is an ecclesiastical doctrine concerning the respect and authority that is due to the pope from other bishops and their sees.
English academic and Roman Catholic priest, Aidan Nichols, wrote that "at root, only one issue of substance divides the Orthodox and the Catholic Churches, and that is the issue of the primacy."