According to Catholicism, is the Body of Christ the same as the Bride of Christ? Are there any Catholic teaching that differentiates between the “Body of Christ” (Church) and the “Bride of Christ”?  

Eve was taken from the Body of the First Adam, will the Bride of Christ be taken from the body (Church) of the Second Adam (Jesus Christ)?
In a word, No: there is no Catholic teaching which differentiates the Body of Christ and the Bride of Christ. The Catechism of the Catholic Church holds that the Church is the Body of Christ and the Bride of Christ.
Adam prefigures Jesus, the &quot;second Adam&quot;. Just as Adam was perfect and became sinful, so Christ took on sin and conquered the death which Adam brought upon humanity. Just as woman was taken out of man, so the Bride of Christ is united to him in one Body which is the Church. This is the doctrine expounded by St Augustine and quoted in the Catechism:

CCC 788 When his visible presence was taken from them, Jesus did not leave his disciples orphans. He promised to remain with them until the end of time; he sent them his Spirit.218 As a result communion with Jesus has become, in a way, more intense: &quot;By communicating his Spirit, Christ mystically constitutes as his body those brothers of his who are called together from every nation.&quot;219
CCC 789 The comparison of the Church with the body casts light on the intimate bond between Christ and his Church. Not only is she gathered around him; she is united in him, in his body. Three aspects of the Church as the Body of Christ are to be more specifically noted: the unity of all her members with each other as a result of their union with Christ; Christ as head of the Body; and the Church as bride of Christ.
CCC 796 The unity of Christ and the Church, head and members of one Body, also implies the distinction of the two within a personal relationship. This aspect is often expressed by the image of bridegroom and bride. The theme of Christ as Bridegroom of the Church was prepared for by the prophets and announced by John the Baptist.234 The Lord referred to himself as the &quot;bridegroom.&quot;235 The Apostle speaks of the whole Church and of each of the faithful, members of his Body, as a bride &quot;betrothed&quot; to Christ the Lord so as to become but one spirit with him.236 The Church is the spotless bride of the spotless Lamb.237 &quot;Christ loved the Church and gave himself up for her, that he might sanctify her.&quot;238 He has joined her with himself in an everlasting covenant and never stops caring for her as for his own body:239

This is the whole Christ, head and body, one formed from many . . . whether the head or members speak, it is Christ who speaks. He speaks in his role as the head (ex persona capitis) and in his role as body (ex persona corporis). What does this mean? &quot;The two will become one flesh. This is a great mystery, and I am applying it to Christ and the Church.&quot;240 And the Lord himself says in the Gospel: &quot;So they are no longer two, but one flesh.&quot;241 They are, in fact, two different persons, yet they are one in the conjugal union, . . . as head, he calls himself the bridegroom, as body, he calls himself &quot;bride.&quot;242

218 Cf. Jn 14:18; 20:22; Mt 28:20; Acts 2:33.
219 Lumen Gentium 7.
234 Jn 3:29.
235 Mk 2:19.
236 Cf. Mt 22:1-14; 25:1-13; 1 Cor 6:15-17; 2 Cor 11:2.
237 Cf. Rev 22:17; Eph 1:4; 5:27.
238 Eph 5:25-26.
239 Cf. Eph 5:29.
240 Eph 5:31-32.
241 Mt 19:6.
242 St. Augustine, Enarrationes in Psalmos 74:4:PL 36,948-949.