Badges are numerical indicators of how many items are associated with an element (a link) and labels are used to provide additional information about something. A tag is a word or a group of words temporarily attached to an item, a SEO tool.
See this explanation on Atlassian Design Guidelines:
Badges provide quick visual identification for numeric values such as tallies and other quantities. They are not used for anything other
than integers. To call out tags or other high-visibility
attributes, use Labels.
Labels, like mentions and lozenges, are a way of visually tagging UI objects for quick recognition and navigation. They are used in taxonomies (tags) to provide an ad-hoc, user-generated scheme for classification and searching, or in multi-select controls to indicate already locked-in elements.
Labels can include an action icon (usually 'remove'). Bear in mind
that they increase the amount of visual noise, particularly in
combination with other visual tagging elements. They should be short
and not require line-wrapping.