If you read all of the apostles words you will find that all are not exactly the same, though the message is. Each wrote as he saw fit for the people of their time. Just as we see something or hear something and then relate it to others in written word or in speech, what we relate is true.
The book of Acts and Matthew are saying the same thing. Christ is the authority as given him by the father, the Holy Spirit sanctions the baptism so that it may be written in the Book of Heaven.
The Mikveh (baptism by water) is a ritual carried out by a qualified Jew to welcome a believer (usually a gentile) into the Congregation and Faith of Israel. Qualifications requires the belief and obedience of the Torah. Since gentiles of the christian churches are not of the Faith of Israel nor of the Congregation of Israel, they are not a part of Israel's Covenants. The gentiles, therefore, are making a false claim to an Office and the functions of that Office that belongs to Israel. The BAPTISM by FIRE was also promised to Israel and not to the church. For a gentile to be baptized by the HOLY SPIRIT, he has to be a part of the Covenant/Treaty of Israel.