Today is the feast of St. Stephen the Protomartyr, the feast is a Double of the Second class with a simple Octave.
Many saints, originally more than now, were celebrated after the Nativity of the LORD. These were described as the 'comites Christi' . e.g. St. James the Lesser and King David. In 'modern' calendars we are left with St. Stephen, St. John the Evangelist, and the Holy Innocents.
St. Stephen's Day was commemorated at Second Vespers of the Nativity. (Special rules apply to Vespers for the Octave of the Nativity). The Office is proper and mattins has three nocturns of nine lessons. The Nativity of the LORD is commemorated at Lauds, Mass and Vespers. Hymns of Iambic metre have the special tone and Doxology in honour of the Incarnation.
At Mass, sung after Terce, the Gloria and Credo are sung. The preface and communicantes are of the Nativity.
Vespers are Second Vespers of the Nativity, but from the chapter they are of St. Stephen with a commemoration of St. John the Evangelist and, as mentioned earlier of the Octave of the Nativity of the LORD.
Following the 'liturgical books of 1962' the Doxology in honour of the Incarnation is omitted at the hymns of the Little Hours. The Little Hours also have ferial antiphons and psalms and at Prime the short lesson is of the 'Christmas season' rather than of the feast. At Vespers there is a commemoration of the Sunday within the Octave but not of St. John. In the traditional rite St. John's feast takes the place of the Sunday