I do not claim to be a Biblical scholar, but in the Jamieson-Fausset-Brown Bible Commentary, their commentary on this verse says:
'James, the Lord's brother—This designation, to distinguish him from James the son of Zebedee, was appropriate while that apostle was alive. But before Paul's second visit to Jerusalem (Ga 2:1; Ac 15:1-4), he had been beheaded by Herod (Ac 12:2). Accordingly, in the subsequent mention of James here (Ga 2:9, 12), he is not designated by this distinctive epithet: a minute, undesigned coincidence, and proof of genuineness. James was the Lord's brother, not in our strict sense, but in the sense, "cousin," or "kinsman" (Mt 28:10; Joh 20:17). His brethren are never called "sons of Joseph," which they would have been had they been the Lord's brothers strictly.'
So in answer to whom Paul was referring, he was James the Good, First Bishop of Jerusalem, and kinsman to Jesus Christ.
Actually....the one (James) that was beheaded was a cousin. You can prove this quite easily.
He was the brother of John: [Acts 12:2] And he killed James the brother of John with the sword.
At the crucifixion: [John 19:25] Now there stood by the cross of Jesus his mother, and his mother's sister, Mary the wife of Cleophas, and Mary Magdalene.
[Mark 15:40] There were also women looking on afar off: among whom was Mary Magdalene, and Mary the mother of James the less and of Joses, and Salome.
[Matthew 27:56] Among which was Mary Magdalene, and Mary the mother of James and Joses, and the mother of Zebedees children.
From the above three scriptures we have determined that Salome is the mother of Zebedee's children and also the sister of Mary. This would make her "Aunt Salome" to Our Lord.
[Matthew 4:21] And going on from thence, he saw other two brethren, James the son of Zebedee, and John his brother, in a ship with Zebedee their father, mending their nets; and he called them.
We now know that James and John are first cousins to Our Lord. This also explains why Our Lord gave the care of His mother to John....a close family member. [John 19:25-27] Now there stood by the cross of Jesus his mother, and his mother's sister, Mary the wife of Cleophas, and Mary Magdalene. When Jesus therefore saw his mother, and the disciple standing by, whom he loved, he saith unto his mother, Woman, behold thy son! Then saith he to the disciple, Behold thy mother! And from that hour that disciple took her unto his own home. The disciple of course was John.
Jesus had a very tentative relationship with His blood siblings. This is demonstrated quite remarkably in [John 7:1-5] After these things Jesus walked in Galilee: for he would not walk in Jewry, because the Jews sought to kill him. Now the Jew's feast of tabernacles was at hand. His brethren therefore said unto him, Depart hence, and go into Judaea, that thy disciples also may see the works that thou doest. For there is no man that doeth any thing in secret, and he himself seeketh to be known openly. If thou do these things, shew thyself to the world. For neither did his brethren believe in him.
There are Three things which jump out at you in these verses. These Brethren are not camp followers as they do not believe in Our Lord (verse 5). They are disgruntled and they taunt The Lord by telling him He should go to the Festivals anyway.....knowing that the Jews are out to kill him. They want Him dead (verse 3)! We sometimes forget just how much Our Lord was hated.....even by His own family [Mark 6:3-4] Is not this the carpenter, the son of Mary, the brother of James, and Joses, and of Juda, and Simon? and are not his sisters here with us? And they were offended at him. But Jesus, said unto them, A prophet is not without honour, but in his own country, and among his own kin, and in his own house.
No....the James that was killed by Herod [Acts 12:2] was cousin James. The James who Paul saw in Jerusalem [Galatians 1:19] was the "Now Converted" brother of Our Lord and leader of the Jerusalem Church [Acts 15:13-15].