Pattern Welded shotgun barrels can be classified into three general categories, all starting with strips of iron and steel, but with different manufacturing methodology:

Twist -thin ribbons of layered iron and steel which are NOT twisted before being wrapped around the mandril and hammer forged.

Crolle Damascus in many patterns which are determined by how the iron and steel were 'piled' or layered in the billet and the twisting of the rods.
       Another image

Laminated Steel - a higher ratio of steel to iron mixed together and ‘puddled’ before being formed into rods.

Damascus quality is best judged based on the overall grade/quality of the gun, not the appearance of the Damascus pattern, the name given the barrels by the maker, or the country of origin.

How do you 'read' crolle damascus?
    Crolle Patterns
    Damascus Pattern Classification
 
Smith barrel examples