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
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