Hi Aliwren,
now don't take this as gospel as i'm not 100% sure. There are many more experienced and qualified people on this forum than me, but this is what i have been lead to believe.
Put in simple terms (and please correct me if i'm wrong all you blade smiths)
440c is a stainless metal. This means it is corrosion resistant, not corrosion proof. It has a relatively high chrome content which means it will not rust easily compared to metals with a lower chrome content. However, the payoff is that it will not sharpen up as sharp as a high carbon content metal and will not keep the edge as readily.
D2 is a high carbon content tool steel with a high chrome content as well. So it will sharpen up as well as 01 tool steel and keep the edge as well as having the ability to resist corrosion better than 01 due to the high chrome content. I have been led to believe that it is harder to work for the amatuer blade smith, but an expert should have no such problems.
Damascus is not a type of metal but a method of forging. Damascus blades may have a number of different metals in it. During the forging process these metals are heated up and folded (?) together many times, over and over. This results in the magnificent patterns on the blade. Again, the edge retention and corrosion resistance is dependant on the materials used.
Again, please dont take this as red, but now i have posted this, there may be more experienced people around who may be able to put me right and educate us both!
Hope this helps.