William Greener in his book "The Gun 1834" described the method of making both Stub Twist & Stub Damascus using a mixture of horseshoe nail "Stubs" & chopped coach springs. The horse nails were high grade Wrought Iron. He lamented the fact that horse nail suppliers were beginning to use "Cast" nails which were worthless for use in gun bbls & feared good quality stubs would very soon be unavailable for bbl making. These stubs were according to him those "Pulled" from the horses hooves in re-shoeing. They were not melted down but were cleaned & tumbled & mixed with the coach springs (Steel) chopped into similar size pieces. They were placed in a container & heated to a welding heat, at which time an iron rod was dipped into the mix & a "Gob" brought out as they would stick to the rod & then hammered into a strip. The finished product showed the spiral wrap of "Plain Twist" but not the continious strips, rather a series of short pieces joined in a spiral direction. Stub Damascus used the same iron a Stub Twist, but was twisted in the bar before wrapping. The Parker marked Stub Twist looks like neither. Obviously they used a different terminology than did the early English Makers. Those bbls marked "London Twist" have an appearance very similar, but not necessarily exact, to Stub Twist as pictured in W Greener's book.
Incidently in the "Machinist Trade" low carbon steel is not considered "Tool Steel". Tool Steel is used as a term for steels useful for "Making Tools" which virtually always requires a High Carbon Steel. High Speed Tool Steels are steels with other allowing ingredients which allows the tool to maintain hardness at a higher temp than will just high carbon steel, even though it may be as hard, & possibly capable of taking a "keener edge".