Yep, looks like WP only searches the post_title and post_content.
You may need to hook into a filter to add a custom search to the SQL string. I believe WP contains some filters to modify the SQL, but I’m not sure off the top of my head.
The get_terms function seems to search for name and slug, so this explains the difference. https://core.trac.wordpress.org/browser/tags/4.2.2/src/wp-includes/taxonomy.php#L1899
Hope you can find a solution to extend the WP posts search and I hope to heave cleared up the difference
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