Question: Why is their not the option of saving our search term results in Notepad ++ ?
Simple answer, because it looks like there was no need to do so. Keep in mind that
Notepad++ is mainly an programming editor and as such there is not really
a need to save the search results often.
In regards to your request, it is not clear to me what you want.
Maybe you can clarify it by using examples, screenshots etc…
Cheers
Claudia