I would second the learned Mr. Kass' opinion- a typo. Wonder what happened to the addition Mr. King referred to for the barrels? Also curious, to me, his reference to his employees at that point in time as "blacksmiths" if i read this correctly.
LC Smith (the Mr. Hunter mentioned) dealt with Krupp and Whitworth- at least until WW1 era- but also Crucible, Halcomb Steel and Sanderson Bros. Mr. Houchin's book page 387 details that, apparently Crucible bought both Halcomb and Sanderson Bros.
No mention of Carpenter Steel (Latrobe PA.) in the Houchin's book, but in Lt. Col. Brophy's 1981 book on Smith plans and specs. Carpenter Steel is the main "call-out" for the various parts machined from tool steel(s) and not 1020.
As a "amateur metalurgist" I have always been fascinated by the various barrel steel grades Parker and Smith used. I am guessing that they are were the same basic AISI nickel steel. Would a set of Acme steel barels on a CHE have a higher tensile strength (after stress relieving) than those Trojan steel barrels on Parker's workhorse shotgun??
I think, and this is just a pure guesstimate, not grounded in fact, that just as the grade, checkering and finish of the stock wood in a Smith Grade 1 was different than that found on a Monogram, their sales/marketing folks decided to "upgrade" the barrel steel names to convince their customers they were getting better steel and wood when they bought a Monogram or a BHE- just a guess--