Putting it in very simple terms:
Priority of a bug is decided on the basis of business impact whereas severity is decided on the basis of technical impact
If a bug is business critical, then generally the priority will be high. For example, on a website, if the brand name is misspelled or logo has some issue.
Higher the technical impact of a bug, higher the severity. For example, if a bug requires writing or changing code of a complex functionality that would impact multiple modules and might require a lot of development and testing effort.
That’s why the priority is generally decided or reviewed by product owner or business analyst.
And generally the severity is decided by people on development side ( developer, development lead or technical architect )
For the examples that you have requested in your question, please refer to THIS link. It will provide you examples for below scenarios:
High Severity – High Priority bug
low Severity and High Priority bug
low Severity and low Priority bug