Sine you’re a coder I won;y go into coding and I’ll just give you the outline.
The first thing you need to do is to get the terms for the current post The first thing you need to do is to get the terms for the current post.
Next you do a new WP_Query, including a tax_query to get other posts that are in the same term http://codex.wordpress.org/Class_Reference/WP_Query
and finally you loop through the returned posts, if any, to show the list.
Let me know if you need help any of the code that goes with these steps.
