Search Results don't match my Google Custom Search results

This plugin seemed like it was exactly what I needed, but after installing it doesn’t seem to produce the same results on my WordPress site as it does when I go to my Google Custom Search web URL.

For example if you go to any page on our site: i.e. https://www.mennoniteusa.org/about-us/ and type “Junior Youth” into the search you get a list of posts and pages from the site, but it doesn’t include a URL that is supposed to be searched in Google Custom Search.

If you go to the Google Custom Search URL (https://www.google.com/cse/setup/basic?cx=014982525090603060596:qbg_0ocaxr0) you get completely different (and more to what we want) results.

https://www.ads-software.com/plugins/google-cse/