A taxonomy is typically a controlled vocabulary with a hierarchical structure, with the understanding that there are different definitions of a hierarchy. Terms within a taxonomy have relations to other terms within the taxonomy. These are typically: parent/broader term, child/narrower term, or often both if the term is at mid-level within a hierarchy.
Taxonomies are often displayed as a tree structure. Terms within a taxonomy are often called "nodes." A node may be repeated at more than one place within the taxonomy if it has multiple broader terms. This is referred to as a polyhierarchy.
Another type of taxonomy, with a more limited hierarchy, comprises multiple sub-taxonomies or "facets", whereby the top-level node of each represents a different type of taxonomy, attribute, or context. This is used on post-coordinated searching, whereby the user chooses a combination of nodes, one from each facet.
The use of equivalent synonyms or see references may or many not exist in a taxonomy. If a hierarchy is not too large and can be browsed, and especially if there are polyhierarchies, then there is less of a need for nonpreferred variants.
The term taxonomy tends to be used to refer to two different things:
a tree-hierarchical controlled vocabulary lacking more complex relationships found in thesauri or ontologies, or
any kind of controlled vocabulary, especially when applied to the world of enterprise content management and web site information architecture, rather than library science literature retrieval.