List terms from Custom Taxonomy

I have registered a custom post type “Projects” and also registered a custom taxonomy for that Post Type called “Project Categories”. On my home page I have a div in which I would like to list all projects and terms fro the “Project Categories” taxonomy. Currently, I am only able to get the lists of the terms. Can someone tell me why I am unable to get the terms to display. Currently, I have:

<div class="list-container">
    <?php 
    query_posts( array( 'post_type' => 'projects' ) );
    if ( have_posts() ) : while ( have_posts() ) : the_post();
    ?>
    <li><a href="https://wordpress.stackexchange.com/questions/223137/<?php the_permalink(); ?>"><?php the_title(); ?></a></li>
    <?php endwhile; endif; wp_reset_query(); ?>
    <?php $taxonomy = 'project_categories';
    $tax_terms = get_terms($taxonomy);
                            ?>
    <?php foreach ($tax_terms as $cat): ?>
        <li><?php $cat; ?></li>
    <?php endforeach; ?>
</div><!--end list-container-->

Another question I have is, is it better to include the taxonomies inside or outside of the query_posts loop?

You’e not echoing out $cat in your foreach loop in the code you provided.

Change : <li><?php $cat; ?></li> to <li><?php echo $cat; ?></li>

Edit:

get_terms() returns an array of objects. So if you want to display the name of the term in your foreach loop it would be:

<li><?php echo $cat->name; ?></li>