>While your entire contents of the search page is included within the search outcomes web page, it's a distinct page. Note that search outcomes include content from templates displayed on the pages searched. The search results web page is displayed when a search is finished from the search web page, when a search from the regular search field does not exactly match a web page title, or when any parameters or special characters are included in a search string
>Userscriptts is likely to be designed to work on the search outcomes web page however not the search web page, for instance. Wikipedia. The search results page will then have a pull down list to the left of its search box, providing your alternative as, say, a modification of a word or phrase search, or a web page ranking refinement.