The chromium gives the metal its sheen, scratch-resistance and corrosion resistance. The molybdenum gives corrosion-resistance, and helps maintaining a cutting edge.
Although there are myriads of variations in the recipes, there are two main varieties of stainless steel:
The 'surgical' refers to the fact that these types of steel are well suited for making surgical implants and equipment: they are easy to clean and sterilize, strong and corrosion-resistant.
Most surgical equipment is made out of Martensitic steel - it is much harder than Austenitic steel, and easier to keep sharp. Depending on the type of equipment, the recipe is varied slightly to get more sharpness, or strength.
Implants and equipment that is put under pressure (bone fixation screws, prostheses, piercing jewellery), are made out of Austenitic steel, often 316L and 316LVM, because it is less brittle.Martensitic stainless steel
These contain less chromium (12-14%), less molybdenum (0.2-1%), no nickel, about 0.1-1% carbon (giving more hardness, but making the material a bit more brittle)
Martensitic stainless steel is quenched, and magnetic. This is 'series-400' steel.
Austenitic stainless steel
This contains more chromium (16-20%), more molybdenum (2-3%), and 8-12% nickel.
This steel is non-quenched, and non-magnetic. Also known as 'series-300' steel.