I appreciate the link that I provided has lots of information.
Here is the short version.
Plain Twist (and Stub Twist) are 2 of the many patterns that fit under the general category of "Twist" - thin strips of alternating steel and iron which are "stacked" into a "lopin" WHICH IS NOT TWISTED (as is crolle damascus) before being run through a rolling mill at high heat and pressure to form the rod, which is then wrapped around a mandrel and helically welded to form the "rough forged tube"
This is a segment of Plain Twist which happens to show the end on rod when it was added to the ribband - the white is iron and black is steel
So for practical purposes, when a U.S. maker labeled their barrel "Twist", or a lower quality Belgian gun was marked "Laminated Steel", it had the appearance of "Plain Twist"
This a Dr. Gaddy's English Twist, Plain Twist, Common Twist, Birmingham, or “Scelp/Skelp” sample segment, which was referred to as "Wire Twist" by W. Greener in 1835.
It is likely that Parker Bros. DID source some Twist (and Crolle Damascus) from Birmingham for Lifters, but certainly the vast majority of top lever guns had "rough forged tubes" sourced from Belgium.