E W Bullinger has a very extensive explanation in the appendix of his Companion Bible. His dates are as follows. See the tables and details at link.
A.M. = Anno Mundi; i. e. in the year of the world.
B.C. = Before Christ. Reckoned as from 4004 A.M.
A.C. = Anno Christi; i. e. in the year of Christ. Reckoned from the Nativity, in 4000 A.M. and 749-750 A.U.C.
A.D. = Anno Domini; i. e. in the year of the Lord.
A.U.C. = Anno Urbis Conditœ; i. e. the year in which the City (Rome) was founded.
A.M. — B.C.-A.D. — A.C. — A.U.C.
4000 THE NATIVITY 4 | 0 | 749 Herod d.c. end 28 Our Lord b. 15th Tisri=29th Sept. 4 B.C.
1. It thus appears without the shadow of a doubt that the day assigned to the Birth of the Lord, namely, December 25, was the day on which He was “begotten of the Holy Ghost”, that is to say, by pneuma hagion = divine power (Matthew 1:18, 20 marg.), and His birth took place on the 15th of Ethanim, September 29, in the year following, thus making beautifully clear the meaning of John 1:14, “The Word became flesh” (Matthew 1:18, 20) on 1st Tebeth or December 25 (5 B.C.), “and tabernacled (Greek eskenosen) with us”, on 15th of Ethanim or September 29 (4 B.C.).
The 15th of Ethanim (or Tisri) was the first day of the Feast of Tabernacles. The Circumcision therefore took place on the eighth day of the Feast = 22nd Ethanim = October 6-7 (Leviticus 23:33-43). So that these two momentous events fall into their proper place and order, and the real reason is made clear why the 25th of December is associated with our Lord, and was set apart by the Apostolic Church to commemorate the stupendous event of the “Word becoming flesh”—and not, as we have for so long been led to suppose, the commemoration of a pagan festival.
No doubt 12/25 was not the date of birth.