The search engine only affects searches that are entered in the URL bar at the very top of Safari. If you are going to Google's site, then using the website's search field, it will, of course, be a Google search.
For the most part, how the search looks in Safari remains the same no matter which search engine you select. If you tap one of the Suggested Websites, you never see the actual search engine page.
If you tap GO, or select one of the search suggestions you go to that search engines webpage. Most of the search sites look a lot alike; blue theme, some sponsored hits followed by ranked results, adds in the right column. You have to look at the top and check the logo to know for sure where you are.
The exception is Duck-Duck-Go. They use a different layout and an orange theme. They are also the only one that 'promises' to not gather and use your data.
You can get a feel for each of them by selecting them in Safari's settings, then doing a few searches in Safari.
Hold in mind that these settings only affect Safari. Third party browsers like Google's Chrome browser have their own settings, usually in the app. Surprisingly, Chrome does offer search engine alternatives: Yahoo, Bing, Ask, and AOL.
Example of a Duck-Duck-Go search:
Edit: I see that I accidentally missed reading an entire page full of responses. I'll leave this up just in case someone's already read it, or on the off chance that contain some small bit of info not already covered.