Dear Ung,
As I said above, the practice in the Typikon is to have an all-night vigil consisting of Compline and Matins, with Divine Liturgy in the morning. The only exception occurs when 12/24 falls on a Saturday or Sunday, when the Greeks (but not the Slavs) omit Great Compline, and celebrate a vigil consisting of Vespers and Matins, with the Liturgy of St. Basil on Christmas morning. (See, for example, Mother Mary's Festal Menaion, p. 252, for an explanation in English.)
When discussing current Orthodox practice, it's best to start with the relevant Typikon (there isn't a complete translation in English, so far as I know) and go from there; the variations will make more sense.
Yours in Christ,
Jeff
