A (vocal) run is an improvised musical passage that is usually based on a scale and tend to have small intervals between notes. It is mostly melodic and offer some kind of uniformity with the instrumental.
A (vocal) riff is a repeated type of notes that has any kind of intervals. But it can also be based on a scale. It can have a lot of different rhythms in it and is based on an existent musical phrase or theme. A riff is added on a song as an artistic or stylistic choice.
In a common usage, they are considered as synonyms.