Our category and tag endpoints currently live at /wp-json/wp/terms/category and /wp-json/wp/terms/tag on develop.
I think we actually want them them to be /wp-json/wp/categories and /wp-json/wp/tags. The endpoint registration pattern should be similar to https://github.com/WP-API/WP-API/pull/820/files#diff-55d3bf5e833c76ee6e3c2f4be15fa1cdR84
Prompted by: #813 (comment)