Defect Severity determines the defect's effect on the application where as Defect Priority determines the defect urgency of repair.
Severity is given by Testers and Priority by Developers
1. High Severity & Low Priority : For example an application which generates some banking related reports weekly, monthly, quarterly & yearly by doing some calculations. If there is a fault while calculating yearly report. This is a high severity fault but low priority because this fault can be fixed in the next release as a change request.
2. High Severity & High Priority : In the above example if there is a fault while calculating weekly report. This is a high severity and high priority fault because this fault will block the functionality of the application immediately within a week. It should be fixed urgently.
3. Low Severity & High Priority : If there is a spelling mistake or content issue on the homepage of a website which has daily hits of lakhs. In this case, though this fault is not affecting the website or other functionalities but considering the status and popularity of the website in the competitive market it is a high priority fault.
4. Low Severity & Low Priority : If there is a spelling mistake on the pages which has very less hits throughout the month on any website. This fault can be considered as low severity and low priority.