These are unique callings which have to do with the
restoration of the Gospel in the Dispensation of the fullness of times.
Joseph Smith and Oliver Cowdery became the First and Second Elders when
they received the Melchizedek Priesthood under the hands of Peter, James,
and John. Note that while they received the priesthood and its keys, they
were not ordained to any specific offices in the priesthood. Rather, they
jointly held the keys that permitted them to ordain each other and others
to the priesthood offices that were necessary to a growing Church after
the Church was established.
One should note here that both Joseph and Oliver
held this priesthood and its keys which include the keys of Presidency
and the Holy Apostleship. Note also that both were witnesses to the restoration
and as such would be called upon to seal their testimonies with their blood.
However, Oliver transgressed and fell from his holy calling. Hyrum Smith,
the Prophet's older brother was called to the office of Second Elder of
the Church. Thus when it was time to become martyrs to the Restoration,
it was Joseph and Hyrum whose blood flowed on the streets of Carthage.
We would note that had the Second Elder not been
martyred with Joseph, it would have been him and not
Brigham Young who
would have succeeded Joseph as the Presiding High Priest in all the world
and thus to the First Presidency.