distinction
An important difference between things or ideas.
A distinction is a difference between things that matters. When a teacher makes a distinction between knowing the answer and understanding the concept, she's pointing out an important difference: you might memorize facts without really grasping how they connect.
Sometimes distinction means excellence that sets someone apart. A student who graduates with distinction has done exceptionally well, earning honors that recognize superior achievement. An artist of distinction has produced work that stands out from others in meaningful ways.
The word can also describe a special quality or characteristic. The distinction of being the first person to climb a mountain, or the distinction of being the only student in your school to win a national competition, marks you as unique in a specific way.
When you draw a distinction, you're identifying a difference that matters. There's a distinction between being scared and being cautious: one is an emotion, the other is a thoughtful approach to risk. Without making such distinctions, we'd lump different ideas together and miss important details. A distinctive trait is one that makes something recognizable and different, like a friend's distinctive laugh you can pick out in a crowded room.