Though I'm not a teacher, I'm a native speaker of English. To me, a distinction can imply that something or someone is markedly different or special. For example, a novelist who has won the Nobel Prize in Literature won it because his or her collection of literary works were, at least, uncommonly good. This is an understatement. According to many people, the quality of said work is very great. The Vampire Diaries is different from other vampire novels because of details like the plot, writing style, or other elements, but the differences between this and other series can vary. The word difference does not have to describe the differences between black and white; it can describe the differences between shades of grey that look very similar. If you listen to Maria Callas' distinct timbre on YouTube then listen to other dramatic coloraturas like Joan Sutherland, you might notice that Maria Callas had a very different voice. It is distinguished and distinct since there aren't many voices like hers. Her voice was unique in the opera world, and she is called La Divina by some for her fantastic, uncommon, contributions to opera. In short, imagine distinction as a set of differences between two objects that are very great in magnitude like arctic versus subtropical climates. Imagine differences as a list of things that are not the same between two things or people, of any magnitude. Have you researched the phrase "distinction without a difference?"

The two words have similar, but different, meanings. A distinction is a characteristic that makes something or someone special or unique in some context. A difference between two things is how they are not the same. Hillary Clinton has the distinction of being the first woman nominated by a major party for president of the United States. The difference between Hillary Clinton and other major party nominees is that she is a woman.