(See Priesthood Restoration, Oath and Covenant. See also TG Entry: Levitical. Undated entry, assumed near study of Oath and Covenant of the Priesthood.)
I Levitical Priesthood
The word “including” in this verse seems to indicate to me that there is a separate priesthood called the Levitical Priesthood.
1 THERE are, in the church, two priesthoods, namely, the Melchizedek and Aaronic, including the Levitical Priesthood.
In other words, it seems to me that the Aaronic priesthood was the priesthood conferred upon Aaron and his sons. The Levitical Priesthood was conferred upon the descendants of Levi. President John Taylor taught that it is an appendage to the Aaronic Priesthood.
THE LEVITICAL PRIESTHOOD
WHAT IS THE LEVITICAL PRIESTHOOD?—There were in the days of Moses a tribe of the children of Israel set apart to officiate in some of the lesser duties of the Aaronic priesthood, and their office was called the Levitical priesthood.—JD, 21:364, August 8, 1880.
THE LEVITICAL PRIESTHOOD AN APPENDAGE TO THE AARONIC.—Aaron and his sons held the Aaronic priesthood, and the Levites were given unto them to minister unto them to keep his charge, the charge of the congregation, to do the service of the tabernacle, keep the instruments of the tabernacle, and the charge of the children of Israel…. They seemed to have been an appendage to the Aaronic priesthood to assist in the service of the tabernacle and other duties. Aaron and his male descendants were selected for the priesthood, the other Levites as assistants, or an appendage.—IP, 40-41. (John Taylor, The Gospel Kingdom, p.158)
But the two priesthoods must be so closely linked that there is no need to distinguish between them. Most of the scriptures do not. In fact, when restoring the Aaronic Priesthood, notice that Moroni did not make a distinction, saying
1 UPON you my fellow servants, in the name of Messiah I confer the Priesthood of Aaron, which holds the keys of the ministering of angels, and of the gospel of repentance, and of baptism by immersion for the remission of sins; and this shall never be taken again from the earth, until the sons of Levi do offer again an offering unto the Lord in righteousness.
Kip on Character 