Severity: How the bug impacts the application. How critical defect is and what is the impact of the defect on the whole system’s functionality. The severity is a parameter set by the tester while he opens a defect and is mainly in control of the tester.
Priority: It defines the priority in which the defects should be resolved. if there are multiple defects, the priority decides which defect has to be fixed and verified immediately versus which defect can be fixed a bit later. It is usually set by the lead
High Priority, Low Severity bug :- If the company name is misspelled in the home page of the website,then the priority is high and severity is low to fix it.
High Severity, Low Priority :- Web page not found when user clicks on a link (user's does not visit that page generally)
Low Priority, Low Severity :- Any cosmetic or spelling issues which is within a paragraph or in the report
High Priority, High Severity :- An error which occurs on the basic functionality of the application and will not allow the user to use the system (E.g. user is not able to login to the application)