Search for drupal site using taxonomy
I'm not very clear what you're asking, so I might be on the wrong track. However a basic search returns a set of nodes that match in a particular order; the normal culprits are Apache Solr and Elastic Search, but there are others. For a large site definitely don't use the builtin search, and do investigate using 'search api' if you're not already.

Once you have a set of nodes, it's up to you how to display them. Including the taxonomy terms associated with each node is part of the display logic, rather than the search itself, and should be relatively easy. Have a look at Display Suite for better control of search views if you need it, though it may well be more appropriate to write a custom node render hook.

If you are more interested in something like a tag cloud of terms that the currently matched nodes reference, that is more difficult but I would look at the tag cloud module, with some custom glue logic to link them.

Hope this helps...