Highly recommend this entire section- it will answer your questions. And, being the Catechism, it gives documentation and further reading.
scborromeo.org/ccc/p123a9p3.htm
A few relevant bits:
//830 The word “catholic” means “universal,” in the sense of “according to the totality” or “in keeping with the whole.” The Church is catholic in a double sense:
First, the Church is catholic because Christ is present in her. "Where there is Christ Jesus, there is the Catholic Church."307 In her subsists the fullness of Christ’s body united with its head; this implies that she receives from him "the fullness of the means of salvation"308 which he has willed: correct and complete confession of faith, full sacramental life, and ordained ministry in apostolic succession. The Church was, in this fundamental sense, catholic on the day of Pentecost309 and will always be so until the day of the Parousia.
…
Who belongs to the Catholic Church?
836 "All men are called to this catholic unity of the People of God. . . . And to it, in different ways, belong or are ordered: the Catholic faithful, others who believe in Christ, and finally all mankind, called by God’s grace to salvation."320
837 "Fully incorporated into the society of the Church are those who, possessing the Spirit of Christ, accept all the means of salvation given to the Church together with her entire organization, and who - by the bonds constituted by the profession of faith, the sacraments, ecclesiastical government, and communion - are joined in the visible structure of the Church of Christ, who rules her through the Supreme Pontiff and the bishops. Even though incorporated into the Church, one who does not however persevere in charity is not saved. He remains indeed in the bosom of the Church, but ‘in body’ not ‘in heart.’"321
838 "The Church knows that she is joined in many ways to the baptized who are honored by the name of Christian, but do not profess the Catholic faith in its entirety or have not preserved unity or communion under the successor of Peter."322 Those "who believe in Christ and have been properly baptized are put in a certain, although imperfect, communion with the Catholic Church."323 With the Orthodox Churches, this communion is so profound "that it lacks little to attain the fullness that would permit a common celebration of the Lord’s Eucharist."324//
Also covered: How are we to understand the truth often spoken by our Church Fathers, “Outside the Church there is no salvation”
