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