Brant A. Gardner discusses the Melchizedek material in Alma 13 and Hebrews; notes that there are important differences between Alma 13 and Hebrews 7.
Brant A. Gardner, Second Witness: Analytical and Contextual Commentary on the Book of Mormon, 6 vols. (Salt Lake City: Greg Kofford Books, 2007), 4:221-22
At this point, we must now consider how Paul and Alma use the Melchizedek figure. There are certainly some similarities, sometimes Alma’s language depends on Joseph’s reading of Paul. However, there are marked differences in the conception and development of the arguments.
First, the story of Melchizedek must have been available to the Nephites. Apparently the brass plates contained some of the material to which Paul refers, but which is not in the Old Testament. Second, the priesthood of Melchizedek had already been called into service as the model for Nephite priesthood. This is evident in that Alma assumes that the priesthood he claims is legitimate through Melchizedek while Paul makes that argument. This is a subtle but important difference. Alma is assuming what Paul must prove. Bot Paul and Nephi had the truth, but neither belonged to the lineage of Levi or Aaron with its traditional claims on priesthood. While Nephi never tells us of his solution, Alma makes it clear that the priesthood had been traced to Melchizedek; Melchizedek’s priesthood had been used to teach the Nephite gospel.
While Paul and Alma deal with the concept of authority. Paul focuses his effort on proving the connection. Alma not only accepts the connection but assumes that his audience does as well and goes on to underscore an entirely different point: the need for repentance and belief in the Messiah.
This subtle difference also appears in the ways Alma and Paul refer to the order of this priesthood. For Paul, it is a priesthood after the order of Melchizedek which justifies Jesus’s priesthood. For Alma, it is the priesthood after the order of the Son that justifies Melchizedek.