List Categories and Taxonomies in Template.

All regular Post Categories

get_categories( string|array $args = '' );

//returns Array of category objects. See get_terms() for possible $args for filtering returned category objects. 

wp_list_categories(array|string $args = '');
//output categories as linked HTML to each category archive page. Can pass argument of echo=true to output directly.

All Terms in Taxonomy

get_terms( array(
    'taxonomy' => 'post_tag',
    'hide_empty' => false,
) );
//returns Array of category objects. 

See possible parameters to get_terms().

No single function to get all terms as links. Example below to loop through get_terms() result with links.

$curr_term = get_query_var( 'term' ); //taxonomy term slug for page you are on

$terms = get_terms( array(
   'taxonomy'   => 'event-categories',
   'hide_empty' => true,
   'orderby'    => 'name',
) );
foreach( $terms as $term ) :
   $class = '';
   if($term->slug == get_query_var( 'term' ) ) {
      $class = 'current-cat'; //if is same as current term add class so can highlight it in list.
   <li class="<?php echo $class; ?>"><a href="<?php echo get_term_link($term); ?>"><?php echo $term->name; ?></a></li>
<?php endforeach; ?>