The 12 days of Christmas is not just English, but a universally Western custom - the 12 days begin with Christmas, and end with Epiphany (which is both the Baptism of our Lord in the river Jordan, and the fulfillment of the enlightenment of the Nations with the coming of the Magi.)
The 12 days and their Western names (in the English use) are:
Dec. 25 Nativity of Our Lord Jesus Christ/St. Anastasia, Virgin Martyr
Dec. 26 St. Stephen, Protomartyr
Dec. 27 St. John, Apostle and Evangelist (Blessing of Wine)
Dec. 28 Holy Innocents, Martyrs
Dec. 29 St. David, King and Prophet
Dec. 30 Within Christmas Octave
Dec. 31 St. Silvester, Bishop and Confessor/Middle lessons of the Nativity of Our Lord.
Jan. 1 Circumcision of Our Lord
Jan. 2 Octave of St. Stephen, Protomartyr
Jan. 3 Octave of St. John, Apostle and Evangelist/St. Genevieve of Paris
Jan. 4 Octave of Holy Innocents, Martyrs/St. Titus
Jan. 5 S. Edward, King and Confessor, Twelfth Night (Great Blessing of Water)
Jan. 6 Epiphany of Our Lord (Blessing of Houses and Chalk)
I've been at Byzantine rite parishes where they also taught '12 days of Christmas' from Christmas to the Eve of Theophany. Never heard of only 7 days for Byzantine rite, unless it is related to the Western rite custom of the 'Octave' where a feast is celebrated for the 7 days following - 8 days in all, an 'octave'