Objection 1. It seems that the three kinds of Baptism are not fittingly described as Baptism of Water, of Blood, and of the Spirit, i.e. of the Holy Ghost. Because the Apostle says (Ephesians 4:5): "One Faith, one Baptism." Now there is but one Faith. Therefore there should not be three Baptisms.
Objection 2. Further, Baptism is a sacrament, as we have made clear above (Question 65, Article 1). Now none but Baptism of Water is a sacrament. Therefore we should not reckon two other Baptisms.
Objection 3. Further, Damascene (De Fide Orth. iv) distinguishes several other kinds of Baptism. Therefore we should admit more than three Baptisms.
On the contrary, on Hebrews 6:2, "Of the doctrine of Baptisms," the gloss says: "He uses the plural, because there is Baptism of Water, of Repentance, and of Blood."
I answer that, As stated above (Question 62, Article 5), Baptism of Water has its efficacy from Christ's Passion, to which a man is conformed by Baptism, and also from the Holy Ghost, as first cause. Now although the effect depends on the first cause, the cause far surpasses the effect, nor does it depend on it. Consequently, a man may, without Baptism of Water, receive the sacramental effect from Christ's Passion, in so far as he is conformed to Christ by suffering for Him. Hence it is written (Apocalypse 7:14): "These are they who are come out of great tribulation, and have washed their robes and have made them white in the blood of the Lamb." In like manner a man receives the effect of Baptism by the power of the Holy Ghost, not only without Baptism of Water, but also without Baptism of Blood: forasmuch as his heart is moved by the Holy Ghost to believe in and love God and to repent of his sins: wherefore this is also called Baptism of Repentance. Of this it is written (Isaiah 4:4): "If the Lord shall wash away the filth of the daughters of Zion, and shall wash away the blood of Jerusalem out of the midst thereof, by the spirit of judgment, and by the spirit of burning." Thus, therefore, each of these other Baptisms is called Baptism, forasmuch as it takes the place of Baptism. Wherefore Augustine says (De Unico Baptismo Parvulorum iv): "The Blessed Cyprian argues with considerable reason from the thief to whom, though not baptized, it was said: 'Today shalt thou be with Me in Paradise' that suffering can take the place of Baptism. Having weighed this in my mind again and again, I perceive that not only can suffering for the name of Christ supply for what was lacking in Baptism, but even faith and conversion of heart, if perchance on account of the stress of the times the celebration of the mystery of Baptism is not practicable."
Reply to Objection 1. The other two Baptisms are included in the Baptism of Water, which derives its efficacy, both from Christ's Passion and from the Holy Ghost. Consequently for this reason the unity of Baptism is not destroyed.
Reply to Objection 2. As stated above (Question 60, Article 1), a sacrament is a kind of sign. The other two, however, are like the Baptism of Water, not, indeed, in the nature of sign, but in the baptismal effect. Consequently they are not sacraments.
Reply to Objection 3. Damascene enumerates certain figurative Baptisms. For instance, "the Deluge" was a figure of our Baptism, in respect of the salvation of the faithful in the Church; since then "a few... souls were saved in the ark [Vulgate: 'by water'," according to 1 Peter 3:20. He also mentions "the crossing of the Red Sea": which was a figure of our Baptism, in respect of our delivery from the bondage of sin; hence the Apostle says (1 Corinthians 10:2) that "all... were baptized in the cloud and in the sea." And again he mentions "the various washings which were customary under the Old Law," which were figures of our Baptism, as to the cleansing from sins: also "the Baptism of John," which prepared the way for our Baptism.
Source: Summa Theologica (New Advent)