What is the difference between page rank and Search engine result page?

PageRank is the grade (1 to 10) your web page gets from headmaster Google. SERP is the position of your website in Google's search engine results based on a certain keyword combination.

PageRank is a numeric value that reflects the importance of a page on the World Wide Web. You may also consider it as Google's rating or perhaps 'grade' for your webpage that starts from 1 and goes up to 10. However, on its own, PageRank doesn't carry much weight. It's something like the grade that the teacher endows you for a particular examination.
SERP, as you well know, stands for Search Engine Ranking Page. It usually concerns the (first) page of results that Google gives you in course of your search for a keyword or keyword combination.