Damascus, or "twist" barrels came about because in the early days it was impossible to drill a hole in a long piece of steel or iron, so the only way to make a barrel was to build it up from smaller pieces. The best known of those processes involved wrapping strips of white hot twisted iron and steel around an iron bar called a mandrel, and welding them together by beating the joints with a hammer. The result is a barrel with a distinctive "barber pole" or "candy cane" appearance. The process was said to have originated with sword makers in the Middle East, and it acquired the name "Damascus steel". Just rust coloring or "browning" won't look like Damascus.
Later, other processes were used for thicker rifle barrels, but the Damascus process continued to be used for the thinner barrels of shotguns.
The high labor cost of making the barrels was reflected in the price of the gun, so Damascus barrels came to be associated with the most expensive (and thus the "best") guns. That, plus the undoubted beauty of Damascus barrels, led some makers of the "cheap" solid steel barrels to try to copy the Damascus appearance.
For years, some buyers of high grade shotguns simply refused to believe that solid steel barrels were actually stronger than built-up barrels, but eventually even the old timers were convinced and both Damascus and fake Damascus faded away. Some Damascus barrels made in the old days are still strong and those guns have been fired with modern shells and modern powders. But, as one might expect, over the years, corrosive primer and powder residue seeped into the multitudinous cracks and crevices in those weld joints and ate the iron and steel from inside. Many of those barrels look good on the outside, but are a mass of rust beneath the surface.
In spite of those (mainly English) folks who insist that their Damascus gun barrels are as strong as, or even stronger than, solid steel, I recommend no Damascus guns be fired or at the most, fired only with black powder. Replacement fingers and eyes are in short supply these days.
Jim