I assume you refer to a custom "success event" which is set somewhere on your website/app. that means without more knowledge we can't really help you.
here are some information which might help anyway:
- "search term instances" is a counter for all "hits" (server calls) that contain the eVar "search term"
- "onsite searches" sounds like a custom "success event" (eventX) that is set maybe when a user performs a search
according to the difference I would check the website and perform some searches. can you see the search term and the eventX?