To the caual user, the distinction between a 'taxonomy' and an 'ontology' is less important. But for those professional accountants trying to master the digital financial report; understanding the difference can be very helpful. The actual term one uses is less important. The meaning behind the term one uses can be very important.
A classification system is a logical grouping of something based on some similarity or other criteria. A classification system is a communications tool. A classification system structures information. A classification system can be informal or formal, more rigorously or less rigorously created, readable/usable by computers, or not. A classification system can be a controlled vocabulary.
A dictionary or list is a classification system that has no hierarchy, it is simply a flat inventory of terms with no relations expressed between the terms.
A taxonomy is a classification system which tends to have one hierarchy into which some list of terms is categorized. Categories are basically sets. A taxonomy is a tree of categories of things with only one relation expressed so terms appear in only one location in a hierarchy of categories.
An ontology is a classification system which tends to have more than one hierarchy into which terms are categorized. So an ontology can be thought of as a set of taxonomies. An ontology can express many different types of relations which includes traits/qualities of each term. An ontology is less like a tree structure and more like a graph structure (as defined by network theory). An ontology tends to be a more formal set of well-defined concepts which precisely describes a specific domain.
You can think of a taxonomy or an ontology as being the same thing or as being different. The term really does not matter. What does matter is understanding that an ontology is far richer discription than a taxonomy and therefore does more.
Although they are called 'taxonomies', both the US GAAP XBRL Taxonomy and the IFRS XBRL Taxonomy are really ontologies. Both have more than one hierarchy (i.e. presentation relations, calculation relations, definition relations). Both are expressed as graph structures, not tree structures (i.e. XBRL networks separate the graphs). For the IFRS taxonomy, numeric relations are expressed via XBRL Formula.
And so even though people say 'taxonomy' when they talk about these two classification systems; think ontology and realize they provide a lot more expressive power than they might first appear to provide.
Also consider how something like the Financial Report Ontology adds additional structure which can be leveraged by machines such as computers.