Final answer:
The ministerial priesthood is the type of priesthood aimed at serving the common priesthood of all baptized Christians by guiding, teaching, and sanctifying the faithful through specific clerical functions.
Step-by-step explanation:
The priesthood that is directed at serving the common priesthood by "unfolding the baptismal grace of all Christians" is the ministerial priesthood. This concept asserts that while all baptized Christians share in the common priesthood by virtue of their baptism, the ministerial priesthood has a distinct role in guiding, teaching, and sanctifying the faithful. This distinction is reinforced by the ritual of ordination, where a member of the church community is consecrated by a bishop to perform clerical functions on behalf of the community.
The ministerial priesthood exists to serve and amplify the spiritual gifts of all the baptized, ensuring the proper administration of the sacraments and the preaching of the Gospel. Although there is a fundamental equality among all believers, the ministerial priesthood is recognized as a specific calling with particular responsibilities within the larger Christian community.