A material test report, or MTR, is the mill's certificate for a heat of steel: its chemistry and mechanical properties. The heat number stamped on the pipe or plate ties the physical material to that report. Traceability means the shop logs those heat numbers when material arrives and records which pieces went into which parts.
A weld map is a drawing of the assembly with every weld numbered. Against each number, the shop records the welder, the procedure used, the date, and the inspection result. If a weld is ever questioned, the map answers who made it, how, and what was checked.
Welding procedures are the written recipe: process, filler, parameters, preheat, and position ranges. Welders are qualified to those procedures by test coupons, which is how a shop demonstrates that the person on the job can produce the weld the procedure describes.
Nondestructive examination is the verification layer. Visual inspection is always done; radiography, ultrasonic, dye penetrant, or magnetic particle testing are added when the code or the client specification requires them, usually on a percentage of welds.
When all of this is planned from the quote stage, the documentation package is a natural by-product of the work rather than a scramble at the end. Ask for it up front, and expect the shop to deliver it with the steel.