Getting Tags using mySQL query

There is a wp plugin that displays lists categories in a multiple columns on a page. I want to modify this plugin so as to do the same with tags instead of category.

The original code (with category) uses the following query to obtain categories:

$cat_list = (array)$wpdb->get_results("
			SELECT {$tp}terms.term_id as cat_ID,
				{$tp}terms.name as cat_name
			FROM {$tp}terms, {$tp}term_taxonomy, {$tp}term_relationships, {$tp}posts
			WHERE {$tp}term_taxonomy.taxonomy = 'category'
			AND {$tp}term_taxonomy.term_id = {$tp}terms.term_id
			AND {$tp}term_taxonomy.term_taxonomy_id = {$tp}term_relationships.term_taxonomy_id
			AND {$tp}term_relationships.object_id = {$tp}posts.ID
			AND {$tp}terms.term_id = {$tp}term_taxonomy.term_id
			{$exclude_sql}
			GROUP BY cat_name
			ORDER BY cat_name
		");

Obviously, my intuition to replace all the cat references with tag reference and change the code. This is my modified code:

$tag_list = (array)$wpdb->get_results("
			SELECT {$tp}terms.term_id as tag_ID,
				{$tp}terms.name as tag_name
			FROM {$tp}terms, {$tp}term_taxonomy, {$tp}term_relationships, {$tp}posts
			WHERE {$tp}term_taxonomy.taxonomy = 'tag'
			AND {$tp}term_taxonomy.term_id = {$tp}terms.term_id
			AND {$tp}term_taxonomy.term_taxonomy_id = {$tp}term_relationships.term_taxonomy_id
			AND {$tp}term_relationships.object_id = {$tp}posts.ID
			AND {$tp}terms.term_id = {$tp}term_taxonomy.term_id
			{$exclude_sql}
			GROUP BY tag_name
			ORDER BY tag_name
		");

However this results in a null string. Any idea how I can fix this?

Thanks