It depends on the source. In the Oresteia, where their role is central, they are represented as having a single purpose, that of hounding Orestes for the blood sin of killing his mother. However, in the Aeneid Book VII, Juno sends Alecto on a solo mission.
The names of these three Furies are variously translated (Wikipedia is not definitive in this regard) and their individual names seem to indicate that each specializes in punishing a different type of crime.
In many mythologies, particularly Classical Mythology, there is the idea of the tripartite goddess (think "mother", "maiden", "crone") who often represent three aspects of a single entity or idea.
Thus, although the Furies may be thought to possess distinct attributes, they are all aspects of the single idea of vengeance, i.e. righteous "fury".