Short answers, pulled from the story.
The word sacrament originates from the Latin term sacramentum, which was a military oath of allegiance in the ancient Roman Empire. Early Christian writers like Tertullian in the third century repurposed this military term to describe profound believer rites such as baptism and the Eucharist.
The Catholic Church officially recognizes seven sacraments, a doctrine solidified at the Council of Trent between 1545 and 1563. This list includes Baptism, Confirmation, the Eucharist, Penance, Matrimony, Holy Orders, and the Anointing of the Sick.
The Catholic Church limits sacraments to seven while the Eastern Orthodox tradition refuses to limit the number and calls them Sacred Mysteries. The Orthodox Church holds that anything the Church does as Church is in some sense sacramental, though it recognizes seven as the major sacraments.
Protestant reformers like John Calvin and Martin Luther accepted only two sacraments as valid under the new covenant: baptism and the Lord's Supper. The Westminster Confession of Faith further limited the sacraments to these two rites, stripping away the five rites commonly called sacraments by the Catholic Church.
The Religious Society of Friends known as Quakers and the Salvation Army do not practice formal sacraments. These groups believe that all of life has the potential to be the means of God's grace and emphasize inward transformation over external rites.
The Community of Christ recognizes eight sacraments including baptism, confirmation, blessing of children, the Lord's Supper, ordination, marriage, the Evangelist Blessing, and administration to the sick. This count differs from other traditions such as the Latter-day Saint movement which uses the word ordinance instead of sacrament.