stainless
440-C is a widely used stainless steel in the cutlery industry. It is high carbon steel with added chromium which resists patina and rusting. Note - it's stain-LESS, not stain-NOT, so you're still going to want to keep it dry. This steel can also can achieve high levels of hardness so after you establish an edge it tends to stay put.
Stainless steel is only used for the "templated" knife making method.
PRO: easy to maintain
CON: a little more work to get an edge.
high carbon steel
We use "1084" which is an awesome high carbon steel and a classic for use in knife making. It's a little softer than stainless which enables it to take a wicked sharp edge making it a favorite of culinary professionals. Due to its softness however the edge will need more maintenance depending on use (and your cutting board). Cutting foods with acid will also discolor the metal creating a patina which some people like and appreciate. A little abrasive scrub can bring it back to its original sheen. This metal lacks the corrosion resistance of stainless and any moisture left on the blade will begin to rust it way more quickly than you think is possible, but take care of it properly and you will have a kitchen compatriot for life. If considering a knife for a gift we tend to push people to select stainless because a carbon knife can be a little like getting someone a pet.
This steel is used for both the "templated" and "forged" knife making methods.
PRO: edge sharpness
CON: rusts easily
Damascus
Two separate types of steel, high carbon and high nickel are alternated in a stack to form a billet. The billet is heated to 2300º and then "forge-welded" into a solid block under an incredible amount of force. Depending on the desired pattern, the billet can be twisted, cut, reforged and further manipulated to create a beautiful piece of swirly looking metal. At first it's difficult to see that pattern as it is only revealed by dipping the finished knife into ferric chloride acid. This process etches the high carbon steel and leaves the high nickel alone, revealing the pattern. The dark parts are the high carbon and the more silvery lines are the high nickel.
PRO - envious looks from all of your friends
CON - rusts easily