The term 'fugue' refers to both a contrapuntal composition technique and a musical form derived from it. It is constructed on a theme or melody (subject) that is introduced at the beginning of the piece by the first voice, and is subsequently taken by other voices in imitation. The interplay between subject and the counter-subjects and/or free counterpoint in the remaning voices makes up the exposition of the fugue, which recurs a number of times in different keys and modes. The expositions are separated by episodes, which consist of modulatory material based on elements heard of the exposition.
The term fugue comes from the latin fugere -to flee- and fugare -to chase. While in the middle ages the term was used to refer to any work following a canonic procedure, during the Renaissance and Baroque periods it came to denote the fully developed procedure of imitative counterpoint. Johann Sebastian Bach, whose pieces are studied as the cenit of the art of fugal writing, modeled his work after the fugues by Buxtehude and Frescobaldi. The textural simplification brought about by the Classical period meant the rise of other procedures and forms, such as the sonata or the symphony. The pure fugue was somewhat abandoned, though composers such as Mozart and Beethoven continued to study the art of fugue and write whole sections of important works using that technique.
The term 'fughetta' refers to a short fugue, while 'fugato' refers to a fugal-like section inside of a work which is not stricly a fugue.