"I believe" (Apostles' Creed) is the faith of the Church professed personally by each believer, principally during Baptism. "We believe" (Niceno-Constantinopolitan Creed) is the faith of the Church confessed by the bishops assembled in council or more generally by the liturgical assembly of believers. "I believe" is also the Church, our mother, responding to God by faith as she teaches us to say both "I believe" and "We believe".
Source: Catechism of the Catholic Church (Vatican.va)