Well, you could ask: "All I really need is a short answer". But then you would have to be specific on how short an answer you are looking for. I'm not trying to be an ass here. IMHO, You will get better answers if you ask better questions.
My short answer to the difference between a Level C and D simulator:
The level D (normally) has better sound, visual, and more realistic bumps, grinds, and other sensations than the level C. A level D can have individual snow flakes on the screen where a level C could only have the visibility drop to simulate snow.
Just remember that the certification is a minimum level of what the sim can be. The simulator can have much more than the minimum required for certification. Also, if an operator buys a level "D" but only asks for a level "C" certification - then a level C is what they get. Why would they do that you ask? Well if you certify to a level "D" you must maintain to a level "D" standard (read much more expensive than the level C) or your certification will drop to a level C or possibly be De-certified for training all together. Sorry, you only wanted to know a short answer.