D&C 86

To Abraham, the Lord made the covenant -

"...thou shalt be a blessing unto thy seed after thee, that in their hands they shall bear this ministry and Priesthood unto all nations..."  (Pearl of Great Price | Abraham 2:9)

For -

"...in thee (that is, in thy Priesthood) and in thy seed (that is, thy Priesthood), for I give unto thee a promise that this right shall continue in thee, and in thy seed after thee (that is to say, the literal seed, or the seed of the body) shall all the families of the earth be blessed, even with the blessings of the Gospel, which are the blessings of salvation, even of life eternal."  (Pearl of Great Price | Abraham 2:11)

Obviously, the emphasis that his seed and all families on earth would receive the blessings of the priesthood.  It becomes clear that they will be not be blessed because they are the seed of Abraham, but that this blessing would be because of the priesthood that his posterity would administer for John the Baptist taught -

"...begin not to say within yourselves, We have Abraham to our father: for I say unto you, That God is able of these stones to raise up children unto Abraham."  (New Testament | Luke 3:8)

In modern day, the Lord again taught the covenant and promises He made with Abraham -

"...thus saith the Lord unto you, with whom the priesthood hath continued through the lineage of your fathers—
9 For ye are lawful heirs, according to the flesh, and have been hid from the world with Christ in God—
10 Therefore your life and the priesthood have remained, and must needs remain through you and your lineage until the restoration of all things spoken by the mouths of all the holy prophets since the world began."  (Doctrine and Covenants | Section 86:8 - 10)

Again, it is apparent that the priesthood is not men for "your life and the priesthood have remained".  It is clear that the two are seperate and not the same.  And the purpose, responsibility, and blessings of the restored priesthood promised to Abraham becomes apparent as the Lord explains -

"Therefore, blessed are ye if ye continue in my goodness, a light unto the Gentiles, and through this priesthood, a savior unto my people Israel."  (Doctrine and Covenants | Section 86:11)

A "savior" would be one that performs essential work that one cannot do on their own.