What is the difference between PR (page rank) and SERP (Search engine result page)?

PR:
PageRank is a numeric value that represents how important a page is on the web. Let's call it Google's rating or grade for your webpage

SERP:
SERP means Search Engine Ranking Page. This is what you look at multiple times a day. It's the (first) page of results Google gives you when you are searching for a keyword or a keyword combination.

Claiming to become a top SEO freelancer, yet in the dark about the difference between PR (Page Rank) and SERP? Never mind, such slips do occur even amongst seasoned SEO professionals. In any case, this blog post will make the picture so clear that you would probably wonder why such a simple issue had escaped your attention so long.Incidentally, whenever you ask any marketer what PageRank actually stands for, the usual response would be "Isn't it the position of your website in Google?" But that is half the truth.

Google PageRank is a factor used to determine the importance of a web page, the web page you note is not a website or a web page, so we can see that in a website many subpages have higher PageRank than the home page, which is currently on the wrong network definitions in points

SERPs is a term which stands for Search Engine Results Page phrase used to refer to the results pages of search engines (Google, Yahoo, Bing ..) returned when someone performed a search query to the this search engine.

PageRank provides a means to determine the value of a website for any given search term or keyword phrase.PageRank was developed, in order to create an algorithm for Google that would allow the website to rank all web pages based on merit.
A Search Engine Results Page (SERP) is the listing of websites returned when you enter a query into a search engine. The results might include a list of websites with different titles, a link to the page as well as a brief description displaying where the keywords have matched content within said page.