Pastoral care of the sick names the ordinary ministry of visiting, comforting and praying with someone who is ill, distinct from, though closely bound to, the specific sacramental rites some Christian traditions perform at the point of serious illness or death.
The practice has a direct textual root. The New Testament letter of James instructs that the elders of the community be sent for and that they pray over the sick person and anoint them with oil in the name of the Lord, a passage cited across Christian traditions, whether or not a given tradition treats anointing as a sacrament, as the origin of the duty to visit and pray with the sick rather than to leave that visit to chance.
Where a tradition does hold a sacramental rite of anointing, ordinary pastoral visiting is what surrounds it rather than standing apart from it: a priest or chaplain visits, assesses the situation with the person and their family, and only then administers anointing of the sick, and in the Roman Catholic tradition viaticum, communion given to someone believed to be near death, may follow within the same visit or a later one. The rite is the culmination of a pastoral relationship, not a substitute for it, and a visit that ends without any rite at all, simple presence, prayer and conversation, remains the ordinary and far more frequent form the ministry takes.
Pastoral visiting also continues entirely on its own, with no rite attached, as ordinary care for any member of a congregation kept away by illness, carried out in many traditions by lay visitors and congregation members as much as by clergy.