Dictionary of Ichthyology  

caudal fin = the tail fin, aiding movement. Also called the uropterygium. The fin at the posterior end of the vertebral column (but in Centriscidae the hind end of the body rotates so that the caudal fin is ventral, and in some Trachipteridae the upper lobe of the caudal may be dorsal (the separate lower lobe may disappear). In other families, such as the Zoarcidae and Anguillidae, dorsal, caudal and anal fins are united and are externally indistinguishable. Various fin shapes are named abbreviate, acaudal, diphycercal, double emarginate, epibatic, epicercal, gephyrocercal, hemicercal, heterocercal, homocercal, hypobatic, isobatic, isocercal, protocercal, pseudocaudal, truncate, etc. (all q.v.) Abbreviated as C.

Some caudal fin types from Wikimedia Commons: http://commons.wikimedia.org/wiki/File:PletwyRyb.svg.
A = heterocercal, B = protocercal, C = homocercal, D = diphycercal.

Canadian Museum of Nature