The terms “prelude” and “fugue” refer to musical movements. Each movement can stand alone, or they  can be paired or even be part of a set of movements, as in the “suite.” When paired, they are typically written in the same key, and they may or may not have stylistic similarities. 

As a distinct movement, the prelude is one of the earliest stand-alone keyboard works, originating in the  mid-15th century. Either secular or religious, the prelude acted as a musical preface or introduction, and was eventually expanded to strings and other instruments. Preludes are usually short and somewhat light in style. 

The fugue is an elaborate and usually complex work based upon imitative counterpoint. A singular melody is duplicated, overlapped, expanded, truncated, transposed, inverted and even reversed. The harmony of the fugue is a by-product of the horizontal texture of the melodies. Fugues often consist of more than one theme, lending an additional challenge to both the player and the listener. Though challenging, the pairing of preludes and fugues makes a logical and satisfying musical experience. 

The undisputed master of the Prelude and Fugue as a musical form was Johann Sebastian Bach  (1685-1750). In his lifetime he published not just one, but two complete sets called The Well Tempered  Clavier. A “complete set” consists of a prelude and a fugue for every possible key, both major and minor;  there being 12 major keys and 12 minor keys in our diatonic system of music, the result is 48  movements. Many composers have worked in preludes and fugues, but very few have published complete sets. Paul Hindemith published his Ludas Tonalis in 1943, and Dmitri Shostakovich his Op. 87 set in 1951.