Create another TAG widget for posts

You’ll need to use register_taxonomy with hierarchical set to false:

function add_custom_taxonomies() {
// Add new "Locations" taxonomy to Posts
register_taxonomy('keyword', 'post', array (
        'hierarchical' = false
    ));
}
add_action( 'init', 'add_custom_taxonomies', 0 );

For more information:
WordPress API
Tutorial @ Smashing magazine