In biblical theology, there is the concept of a “type” and its “antitype.” The term “type” comes from the Greek word τυπικως which is actually used in the Greek New Testament:
Now all these things happened unto them for ensamples (τυπικως): and they are written for our admonition, upon whom the ends of the world are come. (1 Cor 10:11)
The term τυπικως is defined by Greek lexicons such as Thayer as "by way of example (prefiguratively)." The fulfillment of a type, an antitype, is a fulfillment which is greater than the type itself. As one potent example, one Old Testament type of Christ is the brazen serpent, which we read about in Num 21, which the Lord commissioned Moses to make and lift up as a means of physical salvation to the Israelites. In the Gospel of John, the author understood this event to be a prefigurement of a “type” of the crucifixion:
And as Moses lifted up the serpent in the wilderness, even so must the Son of man be lifted up: that whosoever believeth in him should not perish but have eternal life. For God so loved the world that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. For God sent not his Son into the world to condemn the world; but that the world through him might be saved. (John 3:14-17)
Jesus was prefigured by the brazen serpent in many respects—both were “lifted up” and both offered salvation to people. However, the life and death of Jesus was much greater than the Old Testament type found in the brazen serpent—the “salvation” the brazen serpent was physical/temporal, but the salvation offered by and through Christ is eternal life; furthermore, the brazen serpent was only for national Israel, while the atoning sacrifice of Christ was for the entire world. Here we see the relationship between a type and its antitype—important parallels, but the latter is, especially on a soteriological level, much greater.
A type/antitype argument can be made in favour of baptism being salvific. The following comes from an essay on Alexander Campbell, a leading 19th-century advocate of baptismal regeneration, and his arguments in favour of the doctrine following this line of reasoning:
Campbell states what the order of the “ancient gospel” is: first a belief in Jesus; next immersion; then forgiveness; then peace with God; then, joy in the Holy Spirit.” This is Campbell’s conclusion after three articles of argumentation.
He begins the explanation of the design of baptism by noting its relationship in typology, particularly basing his reasoning upon Hebrews 10:22. He asserts, as a thesis, that “Christian immersion stands in the same place in the Christian temple, or worship, that the laver, or both [bath] of purification stood in the Jewish; viz. BETWEEN THE SACRIFICE OF CHRIST AND ACCEPTABLE WORSHIP.” Just as the High Priest had to wash on the day of atonement before entering the Holiest of Holies, so the believer, before he can worship acceptably, must also have his body washed in the rite of baptism. Calling upon John 3:5, Titus 3:5; and Ephesians 5:26, Campbell concludes that Christian immersion is the antitype of the bath of purification for priests in the Old Testament. This is signaled by the use of the term “washing” itself.
Since baptism corresponds to an Old Testament “ablution,” Campbell demonstrates the New Testament “plainly” affirms that “God forgives men’s sins in the act of immersion.” He argues that disciples were conscious of a particular moment when their sins were remitted, and “a certain act by, or in which their sins were forgiven.” That act was the washing which they could remember or forget. Campbell introduces Acts 2:38 to verify this connection between remitted sins and baptism. There Peter “made repentance, or reformation, and immersion, equally necessary to forgiveness,” and if no other word were written on the subject, Peter’s command there would be “quite sufficient.” In consequence of what Peter says here Campbell believers that “in the very instant in which” a person is “put under the water,” he receives “the forgiveness of his sins and the gift of the Holy Spirit.” Consequently, “Christian immersion is the gospel in water.” (John Mark Hicks, “The Recovery of the Ancient Gospel: Alexander Campbell and the Design of Baptism,” in David W. Fletcher, ed. Baptism and the Remission of Sins: An Historical Perspective [Joplin, Miss.: College Press Publishing Company, 1992], 111-70, here, pp.149-50).
If the type/antitype relationship exists between the priestly ablutions and water baptism, we can see their external relationship—the priest is cleansed from ritual impurity by immersion, and a Christian is immersed ritually. However, only by understanding baptism to be salvific can baptism be a true antitype of the priestly ablutions. If one were to hold to a purely symbolic view of baptism, a la Zwingli, Calvin, and much of modern Evangelical Protestantism, baptism was just as (non-)salvific as the priestly ablutions, which would make the Old Testament type as being just as great, vis-à-vis salvation, as its New Testament fulfillment. Latter-day Saint soteriology, however, allows for one to have baptism as the antitype of the priestly ablutions, and, unlike the mere symbolic view of our Evangelical critics, allows the antitype to substantially excel the type thereof.
For further reading on the topic of typology, see Richard M. Davidson, Typology in Scripture: A Study of Hermeneutical Typos Structures (Andrews University Press, 1981)