distinction = a noticeable difference between things or people. A difference you can smell, feel, understand, etc. There is a difference between art and science, but illiterate people are unable to make the distinction between them. There is a difference between formal and informal pronuciation in English, although for non-native speakers often there is no distinction between the two.

I think 'difference' is a more generic term, while 'distinction' hints at something that contrasts two different things. A distinction is not only something that differs, but is something that exists as a defining characteristic of one thing but not the other.