Yes, they are different.
Caloric deficit + no exercise = lose fat, lose muscle
Caloric deficit + exercise = lose fat, maintain or gain muscle
When people speak of "weight loss", they usually mean fat loss. So the second is usually preferred.
There are also other funky things that happen when you consume low calories, such as decreasing bone density, and fat loss actually slowing (your body, it appears, panics because it's starving, and tries to preserve the remaining tissue rather than burn it off), and so on. So in general it's better to have just a small caloric deficit and exercise, than have a huge deficit and not exercise.
And of course, as the guys said, it's not merely calories that matter. There's a difference between 1,000kcal of jam doughnuts, and 1,000kcal of mixed vegies and nuts. The second one will fill you up for longer, and nourish you better.