Commas not displaying in implode

Your problem is that you are defining the $typeName variable as an empty array at the stat of each iteration of the loop, effectively erasing it, then filling that empty array with a single term name, which you implode. You don’t see any commas because you are implodeing a one term array. Move the definition to before the Loop and the implode to after it.

$terms = get_the_terms($post->ID,'category');
$typeName = array();
foreach ( $terms as $term ) {
  $typeName[] = $term->name;
} ?>
<small><?php echo implode(', ', $typeName); ?></small><?php

That said, there are more WordPress-ie ways to do this. WordPress provides a function called wp_list_pluck() that will shorten your labor:

$terms = get_the_terms($post->ID,'category');
$typeName = wp_list_pluck($terms,'name'); ?>
<small><?php echo implode(', ',$typeName) ;?></small><?php

get_the_term_list() may also work for you, though you get hyperlinks and not bare term names:

$terms = get_the_term_list( $post->ID, 'category', $before="", $sep = ', ', $after="" ); ?>
<small><?php echo $terms; ?></small><?php

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