SERP is an acronym for Search Engine Results Page. It is the listing of results based on a keyword query. It is a measure of where your site shows for a target search.
In other words, when the viewer enters a keyword or key phrase into Google, the position your site shows up is its SERP. For example, searching for “web design Roseburg” shows a number two SERP, keeping in mind that the area shown in pale yellow is paid advertising.
PageRank, on the other hand, is a measurement of your web authority, how important your site is. It was named after Larry Page, hence the name, but it is easily confused with the ranking of a page. The Google toolbar includes a PageRank meter which is green and ranks a page 0 to 10. The bar is Google’s assessment of the importance of a web page. It tells you at a glance whether Google considers the page to be a high-quality site.
When doing a search, it is the SERP and not the PageRank that brings a web page to the top of the search.
While both are important, SERP is more important in searches and PageRank is more important in linking.