Cold heading wire is drawn with a controlled reduction, annealed to a fine grain, and coated so it flows in the die without cracking. 304 and 302HQ (with copper for better headability) are the main grades; 316 for marine fasteners; duplex for offshore.
Specify diameter, tolerance, tensile, coating, coil weight and inside diameter, and whether the wire will be used for bolts (larger, lower reduction) or screws (smaller, higher reduction). Ask for a heading test or sample coil before a large order.
The largest stainless fastener clusters are in Taiwan, China, India and Italy; wire makers in those countries carry the widest range of heading qualities.