There are at least three of them: St. James the Greater (meaning older) who was the first bishop at Jerusalem after the Resurrection and Ascension and Pentecost. He was an apostle and he was martyred in about 39 AD, apparently by being thrown from a building. His martyrdom is the only one actually documented in Scripture among the Twelve. He was the brother of St. John the Evangelist (and apostle) and both were sons of Zebedee and they were known collectively as the "Sons of Thunder".
St. James the Less (meaning younger) was also an apostle but did not remain long at Jerusalem. He may have been martyred in Persia but there are no confirmable details of his martyrdom. St. James the Less was NOT St. James the Just. He was the most obscure of the three, apparently.
St. James the Just is believed NOT to have been among the earliest Christians and gained belief in Jesus Christ rather late but he did succeed St. James the Greater as leader of the Church at Jerusalem. St. James the Just was NOT an apostle but he became a martyr in approximately 62 AD when he was stoned to death in the vicinity of the Temple.
One thing that occurs to me at the risk of giving aid and comfort to the reformed amongst us: It seems highly unlikely that James the Just was old enough at his death to be a son of St. Joseph by a marriage earlier than the birth of Jesus Christ since Jesus would have been 66 years old when James the Just was martyred in 62 AD. Jesus was apparently born, according to our calendars in 4 BC the discrepancy being due to different lengths of months in the Julian and Gregorian calendars. Tradition has it that Mary lived to be about 55 years of age,that she was about 13 when Jesus was born, that she therefore ceased to live on earth about ten years after the crucifixion (with St. John the Evangelist in Turkey where their house still stands) which would have had the end of her earthly life in about 39 AD since Jesus was 33 when he was crucified. It is generally believed that St. Joseph was well older than she and since no mention of him contemporaneous to Christ's public ministry appears either in Scripture or tradition, he was likely dead by 26 AD.
It seems unlikely that he had illegitimate children on the side while ostensibly married to Mary, the Mother of Jesus. It also seems rather unlikely that they were divorced and finally, it seems very unlikely that St. James the Just succeeded St. James the Greater at Jerusalem as an infant in 39 AD.
This leads me to believe that, if St. James the Just's father was named Joseph, that father was not St. Joseph; that the added inscription on this ossuary (assuming its authenticity as an ossuary regardless of whose) referencing "brother of Jesus" would be likely a subsequent forgery; that it is literally impossible to prove whether or not the box has anything whatsoever to do with St. James the Just.
This is yet another argument that promises to be endless in the absence of proof of the inauthenticity of the box. It is still a matter of faith and likely to remain so. Give Biblical Archaeological Review every benefit of any and all doubts as to integrity, that does not make the publication infallible. Nor, if the magazine is wrong, does that make the author or the publishers liars, just people honestly mistaken.
Source as to all three of the St. Jameses referenced above: a mid-1970s Britannica. More details when I am more awake tomorrow. Good night, all.