Loop for custom-post-type comparing taxonomy terms for “related” posts?

Question

Change your $args array a little bit:

$args = array(
    'post_type' => array( 'my_projects' ), // it need to get the posts from this post_type
    'order' => 'DESC',
    'posts_per_page' => 5,
    'project_tags' => $term // search taxonomy
);

Other ways to search for taxonomy terms can be found here in the WordPress Codex pages.

Answer on your update:

You can add checks that return false when the function “can’t” return values:

// if the given category doesn't exist
if ( ! is_category( $term ) )
    return false;

// if the given category doen't have posts
if ( ! $loop->have_posts() )
    return false;

The way you set up your code to check if there are related projects will not work the way you set up the function now, try this:

function get_related_projects( $term ) {
    // if the given category doesn't exist
    if ( ! is_category( $term ) )
        return false;

    $return = '';
    $return .= '<ul class="featured-items">';

    $args = array(
        'post_type' => array( 'my_projects' ), // it need to get the posts from this post_type
        'order' => 'DESC',
        'posts_per_page' => 5,
        'project_tags' => $term // search taxonomy
    );

    $loop = new WP_Query( $args );

    // if the given category doen't have posts
    if ( ! $loop->have_posts() )
        return false;

    while ( $loop->have_posts() ) : $loop->the_post();
        global $post;

        $figure="";
        if ( has_post_thumbnail()) :
            $figure = sprintf( '<a href="https://wordpress.stackexchange.com/questions/81477/%1$s" title="%2$s">%3$s</a>',
                get_permalink( get_the_ID() ),
                the_title_attribute( array( 'echo' => false ) ),
                get_the_post_thumbnail( get_the_ID() )
            );
        endif;

        $return .= sprintf( '
            <li>
                <figure class="project-image">%1$s</figure>
                <h1 class="title"><a href="%2$s"><span class="goto">a</span> %3$s</a></h1>
            </li>',
            $figure,
            get_permalink( get_the_ID() ),
            get_the_title()
        );
    endwhile;

    wp_reset_postdata();
    $return .= '</ul>'

    return $return;
}

And then use the following code to check the function:

<?php if ( $projects = get_related_projects( "Car" ) ):  ?>
    <em>Related Projects</em>
    <?php echo $projects; ?>
<?php endif; ?>

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