A distinction between similar things is a difference.

Distinction is the quality of being very good or better than other things of the same type.

A distinction is a special award or honour that is given to someone because of their very high level of achievement.

If you say that someone or something has the distinction of being something, you are drawing attention to the fact that they have the special quality of being that thing. Distinction is normally used to refer to good qualities, but can sometimes also be used to refer to bad qualities.