diff --git a/wp-includes/rest-api/endpoints/class-wp-rest-taxonomies-controller.php b/wp-includes/rest-api/endpoints/class-wp-rest-taxonomies-controller.php
index e431d4b743..32c543ce19 100644
--- a/wp-includes/rest-api/endpoints/class-wp-rest-taxonomies-controller.php
+++ b/wp-includes/rest-api/endpoints/class-wp-rest-taxonomies-controller.php
@@ -84,7 +84,7 @@ class WP_REST_Taxonomies_Controller extends WP_REST_Controller {
 				$taxonomies = get_taxonomies( '', 'objects' );
 			}
 			foreach ( $taxonomies as $taxonomy ) {
-				if ( ! empty( $taxonomy->show_in_rest ) && current_user_can( $taxonomy->cap->manage_terms ) ) {
+				if ( ! empty( $taxonomy->show_in_rest ) && current_user_can( $taxonomy->cap->assign_terms ) ) {
 					return true;
 				}
 			}
@@ -113,7 +113,7 @@ class WP_REST_Taxonomies_Controller extends WP_REST_Controller {
 		}
 		$data = array();
 		foreach ( $taxonomies as $tax_type => $value ) {
-			if ( empty( $value->show_in_rest ) || ( 'edit' === $request['context'] && ! current_user_can( $value->cap->manage_terms ) ) ) {
+			if ( empty( $value->show_in_rest ) || ( 'edit' === $request['context'] && ! current_user_can( $value->cap->assign_terms ) ) ) {
 				continue;
 			}
 			$tax               = $this->prepare_item_for_response( $value, $request );
@@ -145,7 +145,7 @@ class WP_REST_Taxonomies_Controller extends WP_REST_Controller {
 			if ( empty( $tax_obj->show_in_rest ) ) {
 				return false;
 			}
-			if ( 'edit' === $request['context'] && ! current_user_can( $tax_obj->cap->manage_terms ) ) {
+			if ( 'edit' === $request['context'] && ! current_user_can( $tax_obj->cap->assign_terms ) ) {
 				return new WP_Error( 'rest_forbidden_context', __( 'Sorry, you are not allowed to manage terms in this taxonomy.' ), array( 'status' => rest_authorization_required_code() ) );
 			}
 		}
diff --git a/wp-includes/rest-api/endpoints/class-wp-rest-terms-controller.php b/wp-includes/rest-api/endpoints/class-wp-rest-terms-controller.php
index ea2d0d19a7..af806b812f 100644
--- a/wp-includes/rest-api/endpoints/class-wp-rest-terms-controller.php
+++ b/wp-includes/rest-api/endpoints/class-wp-rest-terms-controller.php
@@ -380,7 +380,10 @@ class WP_REST_Terms_Controller extends WP_REST_Controller {
 		}
 
 		$taxonomy_obj = get_taxonomy( $this->taxonomy );
-		if ( ! current_user_can( $taxonomy_obj->cap->edit_terms ) ) {
+		if ( ( is_taxonomy_hierarchical( $this->taxonomy )
+				&& ! current_user_can( $taxonomy_obj->cap->edit_terms ) )
+			|| ( ! is_taxonomy_hierarchical( $this->taxonomy )
+				&& ! current_user_can( $taxonomy_obj->cap->assign_terms ) ) ) {
 			return new WP_Error( 'rest_cannot_create', __( 'Sorry, you are not allowed to create new terms.' ), array( 'status' => rest_authorization_required_code() ) );
 		}
 
diff --git a/wp-includes/version.php b/wp-includes/version.php
index 812a99b67d..96f6c543ae 100644
--- a/wp-includes/version.php
+++ b/wp-includes/version.php
@@ -4,7 +4,7 @@
  *
  * @global string $wp_version
  */
-$wp_version = '5.0-alpha-43439';
+$wp_version = '5.0-alpha-43440';
 
 /**
  * Holds the WordPress DB revision, increments when changes are made to the WordPress DB schema.