Is There a Difference Between Taxonomies and Categories?

I’ve been reading the codex for WordPress closely and am confused about the vague definitions between what a Taxonomy is and what a Category is. For that matter, term is also a word that is used in the description of Taxonomies, but seems used in a manner that hints that it isn’t solely limited to a Taxonomy.

Both are described as a way to classify and group together posts. I do understand that Taxonomies are a more general form of categories, but how exactly do they relate to each other?

Is there a subtle difference I’m just not picking up on?

Taxonomies, as previously described are a collective noun for the following

• category

• post_tag

• post_format

• link_category

• custom taxonomy

The first four are built-in taxonomies, while custom taxonomies are taxonomies that are manually created by the user with register_taxonomy. Custom Taxonomies can be hierarchical (like the build-in taxonomy category) or not (like post tags)

The categories and tags that you create in the back end under the ‘Posts’ screen are in actual fact terms of the taxonomies category and post_tag

You cannot create extra terms in post_format. post_format has built-in terms like post_format_video, post_format_gallery etc. See the codex for all post formats included

EDIT

I have updated the Taxonomies page in the codex to include my diagram and the missing post_format taxonomy