PR is Page Rank which is defined by quality inbound links from other website or webpages to a web page or website as well as say the importance of that site.
SERP stands for Search Engine Result Page is the placement of the website or webpage which is returned by a search engine after a search query or attribute.
PR is now extinct. And rather while it was alive its an element from Google not all other search engines so SERP is always the dominant factor.
PR is the page rank which is calculated by the inbound links to your website.
whereas SERP is Search Engine Result Page which is shown at the of any Search made on search engines.
A search engine results page (SERP) is the page displayed by a search engine in response to a query by a searcher. The main component of the SERP is the listing of results that are returned by the search engine in response to a keyword query.
Pr is the page rank and SERP is the search engine result page.
Difference between PR and SERP is that PR is the page rank which is calculated by the inbound links to your website and search engine results page (SERP) is the page displayed by a search engine in response to a query by a searcher. The main component of the SERP is the listing of results that are returned by the search engine in response to a keyword query.