I think (speculation of course since I didn't write the original message) they are refering to a Stand alone server as something that is coded seperately. Where as dedicated would be the same as the client, but running in server mode.

My reasoning on this is that there is a lot of additional code on the client side that the server could care less about (animations, graphics, fx, cameras...). All of these commands take clock cycles to run, and when it is trying to run them for every entity on the server, it really starts to add up. However if you were careful with your code, you could essentially have two completely seperate games that could run in unison. One for executing server side instructions, and the other for the client. The server side would be stripped down of everything that is not needed so that it could be maximized to handle the extra task of controlling bandwidth. The client would of course be the game which everyone would want to see (particle effects, flares, beams, streaks, animation, big textures, detailed models...).