Yes, there are special hole saws for cutting different materials. Milwaukee advertises their metal cutting hole saws as Bi-metal. The package will tell you which materials they are intended to be used with.
I read the response you received from Henry and agree with drilling the pilot hole completely through the door before using the hole saw. I would not be too concerned with different mandrels for different hole saw manufacturers. I have several hole saws from manufactures such as Milwaukee, Starett and Rigid and they all use the same mandrel.