Both terms are used in Digital marketing industry
-> PR: Stand for page rank, that measure by the quality of that page on the web. It can be increased by the building more links, domain age and many other SEO factors. Today PR is mostly dead, as Google stop considering it for search result and start focusing on domain authority, page authority and root domains.
-> SERP: Stand for search engine result page. When we search anything in search engine (Google) the search result page are called SERP. it may be 1 or 10 or more.
-> PR: Also stand for press release, where someone individual or businesses can post their news like product and service launch ect.