The word "priority" is associated with scheduling, and the word "severity" is associated with standards. "Priority" means something is afforded or deserves prior attention; a precedence established by urgency or order of or importance.
Severity is the state or quality of being severe; severe implies adherence to rigorous standards or high principles and often suggests harshness; severe is marked by or requires strict adherence to rigorous standards or high principles. For example, a severe code of behavior.
The words priority and severity do come up in bug tracking. A variety of commercial, problem-tracking / management software tools are available. These tools, with the detailed input of software test engineers, give the team complete information so developers can understand the bug, get an idea of its severity, reproduce it and fix it. The fixes are based on project priorities and severity of bugs. The severity of a problem is defined in accordance to the end client's risk assessment, and recorded in their selected tracking tool. A buggy software can severely affect schedules, which, in turn can lead to a reassessment and renegotiation of priorities.