Browser vs Search Engine Question

I’m trying to be more mindful about my privacy and security online. I am taking small steps to make my online life more secure and private.

I like to use the Safari browser because it best meets my needs. I like using google as my search but am thinking about using duck duck go.

Will the type of search engine (google, duck duck go, ecosia) make a privacy difference or is it the browser that makes a difference?

For example, …

browser engine privacy search search engine vs