“Severity” is how severe the bug is with regards to the system, the user and the business. So this is the impact of the bug that you find, with regards to the system. Whether it is something that has minimal impact, such as a spelling issue in a paragraph of text, or something more severe such as an application or server error screen that appears when more…
“Priority” on the other hand, I interpret to be the importance that the defect is fixed from the business’ perspective. So in effect, this is setting a level of importance in which the defect should be fixed purely from the context of how it affects the business.
Few very important scenarios related to the severity and priority:
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. (Eg. A site maintaining the student details, on saving record if it, doesn’t allow to save the record then this is high priority and high severity bug.)
High Priority & Low Severity: The spelling mistakes that happens on the cover page or heading or title of an application.
High Severity & Low Priority: An error which occurs on the functionality of the application (for which there is no workaround) and will not allow the user to use the system but on click of link which is rarely used by the end user.
Low Priority and Low Severity: Any cosmetic or spelling issues which is within a paragraph or in the report (Not on cover page, heading, title).