The second form is known as "Benediction the Blessed Sacrament" in which the Host is exposed for public veneration in a monstrance on the altar, and, at the conclusion, the monstrance is used to bless the people.
from A Catholic Dictionary, edited by Donald Attwater, Second edition, revised 1957
Benediction, Apostolic, The.
The solemn public blessing with plenary indulgence which, before 1870, the pope pronounced from the balcony of St. John Lateran on Pentecost or Ascension day, from St. Peter's on SS. Peter & Paul, Maundy Thursday, and Easter day, and from St. Mary Major's on the Assumption. The power to give this blessing and indulgence with a special formula is given to bishops and other prelates twice a year, to priests on special occasions and for general purposes, e.g., Dominican tertiaries may receive it from their director, either as a body or individually, twice a year. All priests must give this blessing, with the formula from the "Rituale," to a sick person who is in danger of death; it conveys a plenary indulgence on the usual conditions
from Modern Catholic Dictionary by John A. Hardon, S.J. Doubleday & Co., Inc. Garden City, NY 1980
Benediction of the Blessed Sacrament
A Eucharistic devotion in the Catholic Church of the Latin Rite. In its traditional form, a priest, vested in surplice, stole, and cope, places on the altar or in the niche above it the consecrated Host in the ostensorium, or monstrance, and then incenses it. O Salutaris Hostia or a similar hymn is usually sung at the beginning of exposition, followed by a period of meditation, praise, and adoration by priest and people. At the conclusion of the ceremony the Tantum Ergo hymn is chanted, with another incensation, and followed by blessing the people with the raised monstrance in the form of a cross. During the blessing the priest wears the humeral veil covering his hands. A small bell is rung during the blessing. The Divine Praises are then sun or recited by priest and people, and the Blessed Sacrament is reposed in the tabernacle. Benediction is commonly held on major feasts and Sundays, also during Lent, during a mission, or retreat or during forty hours' devotions. Other days may be designated by individual bishops. Since the Second Vatican Council the Holy See has simplified the traditional ritual, allowing for a variety of options in the prayers, songs, and readings "to direct the attention of the faithful to the worship of Christ the Lord" (Eucharistiae Sacramentum, 1973, No. 95)