Chateaubriand is actually a dish and not a cut of meat so no Chateaubriand is not the same as Filet Mignon.
Filet Mignon is a cut of meat that is similar to the meat used to make Chateaubriand but it's not the same.
Chateaubriand is a roast made from the center section of the beef tenderloin and served with a white wine demi-glace sauce.
They also both taste very similar but no they are not the same even though they seem the same because they do have a similar look and taste.
But the Chateaubriand is the food that is a dish made with a tenderloin type of steak whereas Filet Mignon is a cut of meat.