Badges are numerical indicators of the number of elements associated with an element (a link) and the labels are used to provide additional information about an element. A tag is a word or group of words temporarily attached to an element, an SEO tool.
See this explanation on Atlassian Design Guidelines:
badges provide quick visual identification for numerical values such as counters and other quantities. They are not used for anything else
than integers. To call Keywords or other high visibility
attributes, use labels.
Labels, such as mentions and diamonds, allow you to visually mark user interface objects for quick recognition and navigation. They are used in taxonomies (tags) to provide an ad-hoc, user-generated schema for classification and search, or in multiple-selection controls to indicate already locked items.
Labels may include an action icon (usually "delete"). Keep in mind
that they increase the amount of visual noise, especially in
combination with other visual marking elements. They should be short
and does not require a return to the line.