I believe the function in fetch_tagbits in functions_bigthree.php is the function you need to edit.
PHP Code:
$tag_array = explode(',', $threadinfo['taglist']);
This explode seperates the taglist found in the thread table into array and the code below put all the tags together like shown on showthread.php.
The tags are insert with the function add_tags_to_thread in functions_newpost.php. Then the tags are exploded with the explode on line 627 of function fetch_valid_tags in functions_newpost.php.
You shouldn't have to edit to tags.php because in this file I believe it pulls all the tags from the tags table.
I didn't really look into changing or delete tags but that covers adding and selecting I believe.