Classification & Composition
There are two main types of hierarchies - classification or composition. Technically, taxonomy is a classification hierarchy - relating ideas or things into types or classes. Another way of relating things or ideas is in a composition hierarchy, by identifiying their parts or aspects.
Classification shows the relationship between a general class (of a thing or idea) and its members or types.
Composition shows the relationship between a complete whole (of a thing or idea) and its parts or aspects.