Hi Darrell,
If you’re Embedding a List of Discourse Topics Into an External Site, you should get re-directed to the corresponding Discourse site topic when you click on a topic from the list, so any changes to the topic will be correctly reflected there.
Updating the topic itself will not generate a new topic in the list.
Does this help answer your questions, or was there a different method you were referring to for embedding the topics on your site?