So you're saying it's not the baptism of John?
John's baptism was a baptism of repentance in preparation for the coming of the Messiah. Christ instituted a new baptism, not one of repentance, but in the name of the Father, Son, and the Holy Spirit which as we read in Scripture is "for the forgiveness of sins" (Acts 2:38), being clothed with Christ (Galatians 3:27), and being buried with Christ (Colossians 2:12). In the Acts of the Apostles, St. Paul encounters a group of John's disciples who knew only of the baptism of John, Paul then explained the Gospel and this group was then given Christian Baptism and Chrismation:
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There he found some disciples. And he said to them, 'Did you receive the Holy Spirit when you believed?' And t hey said, 'No, we have not even heard that there is a Holy Spirit.' And he said, 'Into what then were you baptized?' They said, 'Into John's baptism.' And Paul said, 'John baptized with the baptism of repentance, telling the people to believe in the one who was to come after him, that is, Jesus.' On hearing this, they were baptized in the name of the Lord Jesus. And when Paul had laid his hands on them, the Holy Spirit came on them, and they began speaking in tongues and prophesying. There were about twelve men in all." - Acts 19:2-12
We can know a couple things here:
1) This group though described as "disciples" but they were completely unfamiliar with Christian teaching, being only familiar with the teaching of John the Baptist; we can infer that these were disciples of John, not Jesus; they weren't Christians, but followers of John (there probably were some followers of John the Baptist who never converted to Christianity, some group of which may be the forerunners of the
Mandaean religion).
2) The baptism of John was a "baptism of repentance" the meaning here is as we see in the Gospels, that John was calling his fellow Jews to a state of repentance in preparation for the coming of the Messiah, to ready themselves. With the coming of Jesus, the role of John was reduced, "He must increase, but I must decrease." and Jesus, His work and ministry, fulfills John's and John's work is brought to fruition in Jesus because John's mission and ministry was to point to Jesus.
3) Paul gives them Christian baptism, the Acts of the Apostles often uses the language of being baptized in the name of Jesus Christ, or in the name of the Lord Jesus. Some have tried to argue that this means that the earliest Christians conducted baptisms using this as formulaic, contrary to what we see in Matthew's Gospel where Jesus instructs His apostles to make disciples baptizing them in the three-fold name of Father, Son, and Holy Spirit. The easiest resolution here is that "in the name of Jesus Christ" or "in the name of the Lord Jesus" isn't formulaic so much as it means "by the authority of Jesus Christ". It therefore designating Christian Baptism as distinct from Jewish baptism (tevilah) and John's baptism of repentance.
4) The laying on of hands is something that has always been retained in Christianity, usually with Baptism--called Chrismation. Chrismation is laying on of hands and application of oil as a sign and seal of the Holy Spirit. Baptism and Chrismation--historically--were effectively regarded as one rite, though it was possible for these to happen independently of one another. In fact the Western medieval rite of Confirmation is nothing more than Chrismation being postponed until later, an historical curiosity resulting from a Western quirk in saying that only bishops could lay on hands and apply chrism (oil), since bishops weren't always available at every baptism, it simply became normal in the West for it to happen as late as 12 or 13 years of age--becoming the modern rite of Confirmation. That said, there are still Western churches which include Chrismation as part of the Baptismal rite, in Baptisms I have witnessed in my own Lutheran church baptism is immediately followed by chrism and laying on of hands (we have Confirmation as something entirely different, retaining it as a "churchly rite" for good order in church, but just that, a helpful church ritual and nothing more).
Christian baptism =/= John's baptism. John's baptism anticipates Christian baptism, as it anticipates Christ.
-CryptoLutheran