Many types of fish migrate on a regular basis, on time scales ranging from daily to annually or longer, and over distances ranging from a few metres to thousands of kilometres. Fish usually migrate because of diet or reproductive needs, although in some cases the reason for migration remains unknown.
Classifications can be either fundamental (like biological classification that rests on a phylogenetic basis), or are merely heuristic typologies (as here, about migrations) to assist communication about complex issues. Classifications are judged according to their fundamental accuracy, whether they are convenient or not. Typologies in contrast are essentially arbitrary and their effectiveness is to be judged solely by the problems they solve or create. Secor and Kerr (2009) for example show several typologies that encapsulate various aspects of fish life history.
Migration is a word used in multiple senses. It is important to distinguish "true" migration, i.e. a life-history-structured or at least patterned activity such as seen in anadromous species like salmons, from mere movement or wandering as may happen, say, with euryhaline species that easily move between fresh and salt water but not necessarily or with regularity. "Vertical migration", for example, the phenomenon of plankton and fishes regularly changing their depth throughout the 24h day, is a special usage unlike migrations of (e.g. salmons) that range over distances in migrations that may cover river, lake, and sea, or the great migrations of game through Africa's Serengeti.
Anadromous and catadromous are words that have been commonly used for centuries. They are slightly more narrowly used in the following classification of [truly] migrating fish by Myers 1949:
The "-ous" endings are for the adjectival form of the terms; nouns are obtained by replacing that ending with "-y", e.g. anadromy.