A taxonomy in Drupal (and GovCMS) is a way to classify or categorise certain types of content.
A vocabulary is a group of taxonomy terms. A vocabulary can only be used to categorise one type of content. For example, only the Event categories vocabulary can be used to categorise content of type Event.
These terms and the distinction between them is best illustrated by an example. Page articles can be classified or categorised by the Topics they relate to. The categories or taxonomy terms can be Policies, News or Services. The vocabulary in this example would be called Topics.
To see the list of vocabularies available to use on a site, hover over Structure on the Admin menu then click Taxonomy.
Click on the List terms to the right hand side any of the vocabularies listed to show the list of taxonomy terms it contains.
In the screenshot below, the Topics terms are shown.
When creating (or editing) content of type Page content, authors can add a Topic (taxonomy term) to the content. Only the Topics vocabulary can be used for the Page content type (unless your developers have configured additional vocabularies).