What is the difference between Baptism and Confirmation in the Catholic Church?
Baptism, Confirmation and Holy Communion are the three sacraments that make up what we typically call the sacraments of initiation.
Baptism is the the sacrament of regeneration by which we enter into the life of the Church. Without baptism we can not receive other sacraments.
1267 Baptism makes us members of the Body of Christ: "Therefore . . . we are members one of another." Baptism incorporates us into the Church. From the baptismal fonts is born the one People of God of the New Covenant, which transcends all the natural or human limits of nations, cultures, races, and sexes: "For by one Spirit we were all baptized into one body." - Catechism of the Catholic Church
Baptism cleanses away original sin and any actual sin from the soul and confirmation confirms and strengthens in our faith. Confirmation also fortifies with the gifts of the Holy Spirit.
Confirmation is the continuation of baptism and, together with this and the reception of the Eucharist, forms the sacraments of Christian initiation. Confirmation is understood as the gift of the power of the Holy Spirit to the believer. It helps the baptized believer to become more deeply rooted in the childhood of God, to become more firmly integrated into Christ, to strengthen his connection with the Church, to participate more in their mission and to help to testify in word and deed for the Christian faith. In other words the sacrament of confirmation strengthens and confirms one in the faith which has been regenerated in the waters of baptism.
The Catechism of the Catholic Church defines baptism and confirmation as follows:
The Sacrament of Baptism
1213 Holy Baptism is the basis of the whole Christian life, the gateway to life in the Spirit (vitae spiritualis ianua), and the door which gives access to the other sacraments. Through Baptism we are freed from sin and reborn as sons of God; we become members of Christ, are incorporated into the Church and made sharers in her mission: "Baptism is the sacrament of regeneration through water in the word."
The Sacrament of Confirmation
1285 Baptism, the Eucharist, and the sacrament of Confirmation together constitute the "sacraments of Christian initiation," whose unity must be safeguarded. It must be explained to the faithful that the reception of the sacrament of Confirmation is necessary for the completion of baptismal grace. For "by the sacrament of Confirmation, [the baptized] are more perfectly bound to the Church and are enriched with a special strength of the Holy Spirit. Hence they are, as true witnesses of Christ, more strictly obliged to spread and defend the faith by word and deed."
Confirmation (or Chrismation in the Eastern Church) is the sacrament through which the baptised are sealed with the gift of the Holy Spirit.
The sacrament of Confirmation strengthens the Christian with the gifts of the Spirit to help him or her live out the Christian life. The Catechism of the Catholic Church says “Confirmation brings an increase and deepening of baptismal grace; it unites us more firmly to Christ; it increases the gifts of the Holy Spirit in us; it gives us a special strength of the Holy Spirit to spread and defend the faith by word and action as true witnesses of Christ, to confess the name of Christ boldly and never be ashamed of the cross.” (#1303)
Thus Confirmation in a sense completes the baptism with an outpouring of graces the we initially received in baptism and bring the our sacramental life within the Church as witnesses of the faith to completion.
Confirmation is the completion of the process of initiation into the family of Christ and is preceded by Baptism and the Holy Eucharist. It is one of the 7 Sacraments of Catholicism. Confirmation involves being responsible for one’s faith and actions and is a coming-of-age ceremony. Performed by the Bishop, the confirmation rituals involve laying on of hands as well as anointing with holy oils. In addition, the person chooses a new name which is generally the name of a saint and is added to the Christian name after being confirmed by the Bishop. - Becoming Part Of The Catholic Church: Baptism, First Holy Communion, And Confirmation
The Catechism of the Catholic Church goes on to explain the completion of baptism with confirmation:
The Effects of Confirmation
1302 It is evident from its celebration that the effect of the sacrament of Confirmation is the full outpouring of the Holy Spirit as once granted to the apostles on the day of Pentecost.
1303 From this fact, Confirmation brings an increase and deepening of baptismal grace:
it roots us more deeply in the divine filiation which makes us cry, "Abba! Father!";
it unites us more firmly to Christ;
it increases the gifts of the Holy Spirit in us;
it renders our bond with the Church more perfect;
it gives us a special strength of the Holy Spirit to spread and defend the faith by word and action as true witnesses of Christ, to confess the name of Christ boldly, and never to be ashamed of the Cross.
Recall then that you have received the spiritual seal, the spirit of wisdom and understanding, the spirit of right judgment and courage, the spirit of knowledge and reverence, the spirit of holy fear in God's presence. Guard what you have received. God the Father has marked you with his sign; Christ the Lord has confirmed you and has placed his pledge, the Spirit, in your hearts. (St Ambrose, De myst. 7, 42 PL 16, 402-403.)
1304 Like Baptism which it completes, Confirmation is given only once, for it too imprints on the soul an indelible spiritual mark, the "character," which is the sign that Jesus Christ has marked a Christian with the seal of his Spirit by clothing him with power from on high so that he may be his witness.
1305 This "character" perfects the common priesthood of the faithful, received in Baptism, and "the confirmed person receives the power to profess faith in Christ publicly and as it were officially (quasi ex officio)."