wp_count_terms() │ WP 2.3.0

Count how many terms are in Taxonomy.

Default $args is 'hide_empty' which can be 'hide_empty=true' or array('hide_empty' => true).

Uses: get_terms()
1 time — 0.000664 sec (slow) | 50000 times — 26 sec (slow)

No Hooks.

Return

String|WP_Error. Numeric string containing the number of terms in that taxonomy or WP_Error if the taxonomy does not exist.

Usage

wp_count_terms( $args, $deprecated );
$args(array|string)
Array of arguments that get passed to get_terms().
Default: empty array
$deprecated(array|string)
Argument array, when using the legacy function parameter format. If present, this parameter will be interpreted as $args, and the first function parameter will be parsed as a taxonomy or array of taxonomies.
Default: ''

Changelog

Since 2.3.0 Introduced.
Since 5.6.0 Changed the function signature so that the $args array can be provided as the first parameter.

Code of wp_count_terms() WP 5.9.3

wp-includes/taxonomy.php 
function wp_count_terms( $args = array(), $deprecated = '' ) {
	$use_legacy_args = false;

	// Check whether function is used with legacy signature: `$taxonomy` and `$args`.
	if ( $args
		&& ( is_string( $args ) && taxonomy_exists( $args )
			|| is_array( $args ) && wp_is_numeric_array( $args ) )
	) {
		$use_legacy_args = true;
	}

	$defaults = array( 'hide_empty' => false );

	if ( $use_legacy_args ) {
		$defaults['taxonomy'] = $args;
		$args                 = $deprecated;
	}

	$args = wp_parse_args( $args, $defaults );

	// Backward compatibility.
	if ( isset( $args['ignore_empty'] ) ) {
		$args['hide_empty'] = $args['ignore_empty'];
		unset( $args['ignore_empty'] );
	}

	$args['fields'] = 'count';

	return get_terms( $args );
}

counts (counting of any)

Taxonomies: categories, tags, ...