Change post result style per page

I have a search plugin that lists all post results on a page I specify, however, the theme has a weird way of showing post results which is in these cool circle styles. It is creative for the homepage, however, I just want to have the search results show up in a regular list (title, excerpt, author, date, all in lines like google search results).

All I want to know is, how can I create a custom template page which shows the posts in a list but only if the search results are on that page template? Sort of like an “if this page then show results like this, else, show results by theme default listing style.”

Hope someone can help me! Thanks 😀