Drupal - Configuration export/import doesn't work

Configuration management is exporting exactly what it was designed to do: Export the configuration settings. The actual taxonomy terms themselves are sitting in the taxonomy_term_field_data table in the database.

This is by design as taxonomy terms is the content, not configuration.

Features deals exclusively with configuration and so won't include support for content entities such as taxonomy terms.

^{Source: Exporting of Taxonomy terms.}

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However you can use other modules which may work with content such as Default Content module which supports taxonomy terms. Or check Deploy module for content staging.

For example check out this patch for Default Content module: Drush comand to export all items, once applied, you can export all terms from the specific vocabulary using drush, e.g.

drush dcer taxonomy_term vid my_vocabulary --folder=dest/

See also: How do I export my site structure?