Stainless wire work-hardens as it is drawn, so the same grade can be supplied soft annealed (about 500 to 700 N/mm²), quarter or half hard, hard drawn, or spring temper (1400 to 2200 N/mm² depending on size). The temper decides whether the wire can be bent by hand, formed on a machine or hold a spring.
Spring wire standards (EN 10270-3, ASTM A313) specify tensile by diameter — finer wire is stronger per square millimetre. Ask for the tensile range, not a single number, and for elongation and torsion values if the wire will be twisted or coiled.
Annealing after drawing softens the wire again; bright annealing keeps the surface clean. For deep forming, specify soft annealed and a coating suited to your tooling.