Severity measures the technical IMPACT of a defect on the system; Priority measures the URGENCY of fixing it from a business perspective. They are independent — a defect can be any combination of the two.
SEVERITY (usually set by the tester) reflects how badly the defect breaks functionality: Critical (system crash/data loss), Major, Minor, Cosmetic. PRIORITY (usually set by product/lead) reflects how soon it must be fixed: High, Medium, Low. The four combinations all occur: High severity + High priority (payment fails on checkout); High severity + Low priority (crash on a rarely-used admin edge case); Low severity + High priority (a typo in the company logo/name on the homepage — trivial technically but urgent for brand); Low severity + Low priority (minor cosmetic issue in an obscure screen). Distinguishing them is a classic interview question.
A misspelled company name on the homepage is LOW severity (nothing is broken functionally) but HIGH priority (it's embarrassing and public), while a crash in a rarely-used report is HIGH severity but possibly LOW priority.
Give an example of a LOW severity but HIGH priority defect, and explain why severity and priority differ.