Steve Gardham wrote of the relationship between "Andrew Bardeen" and "Henry Martin." I think it's worth emphasizing that the ballad of Andrew Barton is historical. The following is based on Jackie Cosh, The King with the Iron Belt: The Life of King James IV of Scotland, JC Publications, 2018:

Scotland's King James IV (died 1513) "set out to build a navy that would impress," though he was short of money, and Scotland was not noted for ship-building; he ended up purchasing ships abroad. Fortunately, he "had able captains, including John Barton and his three sons Robert, John, and Andrew." James actually bought half-ownership of a ship from Robert Barton, and Barton also organized supplied for James's ship-building efforts (Cosh, p. 48). John Barton Jr. captained some of these ships. Andrew was a recipient of lands in Fife (Cosh, pp. 48-49).

Originally Andrew Barton fought the Portuguese, not the English, after the Portuguese had attacked John Barton's ships. So James IV gave him a letter of marque to fight the Portuguese in 1507 -- only to suspend it in 1510 when Andrew got mixed up with what sounds like a mixed Portuguese/English fleet. The Bretons were also after him, so he and Robert Barton went to Denmark for a while (Cosh, pp. 49).

The problem was that Andrew Barton seems to have enjoyed being a pirate; he refused to stop his activities. So, when Lord Edward Howard encountered Barton and his two ships the Lion and the Jennet of Purwyn, Howard attacked, winning the battle, killing Barton, and capturing most of his men (Cosh, pp. 49-50).

It should be noted that England and Scotland were officially at peace at this time; James IV had married Henry VIII's sister Margaret Tudor. The peace wouldn't last much longer. This makes it hard to determine Barton's true status. In a legal sense, he was probably a pirate, in that he attacked the commerce of a friendly power, but he was also an officer of James's navy. Barton himself was dead, but the status of his surviving crew probably should have depended on James's response to Henry's complaints about the attack.

Additional information about Barton can be found in Child. As for Edward Howard, note that his father Surrey was the man who, two years later, fought and won the Battle of Flodden (and was given back his Dukedom of Norfolk as a reward). The Lord Howard who led the English fleet against the Spanish Armada was also a member of this family.

I really would consider "Henry Martin" to be "Andrew Barton"; it retains all the actual facts of "Andrew Barton," including the three brothers in Scotland and the fact that Andrew was the one most engaged in piracy. Child was confused by the versions he had found: the "Andrew Barton" versions were long and detailed; the "Henry Martin" versions, apart from changing the name in a way that is easily understood as an error of hearing, were shorter and simpler. But we have a lot more versions now. There simply isn't a dividing line, though it does seem as if the change to "Henry Martin" took place in a version that had gotten shorter and simpler.