Nope, Browser is the tool, the software to reach internet. Like a phone.
Search Engine is more like the phone book of URL reference. And you use it with keywords
The browser is the software to use the internet and a search engine essentially scans the entire accessible web for the words you type in to it and shows you where they are.
Browsers are the app you click on: google chrome, firefox, Microsoft edge, safari
Search engines are a website you go to on that app. If you type something in the top bar of your browser that is not a link, browsers will automatically enter that into a search engine.: google search, Bing, duckduckgo, ecosia, startpage
OS: chromeOS
Phone: stock xiaomi 10
Browser: internet explorer (VM)
Search engine: baidu results served through ask jeeves
Location: Constantly updated via API to Facebook
Cookies: batch downloaded
Send optional data to Microsoft: printed and mailed
OS: EndeavourOS
Phone: Pixel 7 Pro (using GrapheneOS)
Browser: Firefox (Plus uBlock, Plus Pihole, plus Adguard)
Search engine: startpage
location: off (on for specific apps)
cookies: auto declined
send optional data to Microsoft: no even using Windows
OS: kubuntu
Phone: pixel with grapheneis + pihole
Browser: FF (+ublock)
Search engine: searx (hosted by non profit)
Kocation: off
Cookies: avoid when possible
Mail: Infomaniak
Collab software: next cloud
Etc.
nah they still spy on you using the American ways until EU realises and tells them to stop, but it doesn't happen instantly and there's always new bullshit to stop them from doing