Retest whole system or just changes with regression tests
After regression tests are done, bugs are filed and fixed. A new release build is made with bug fixes. Should you re-run regression tests again on new build or is it enough to do only re-testing of the part where there were bug fixes?
If you have an automated regression suite, you should definitely re-run it. If your organization is really on the ball, this will happen automatically along with all the unit tests and other tests as part of your continuous integration process.
If you don't have that luxury, then if you don't see a major risk, then testing only around the areas that were impacted by the bug is acceptable. In that scenario you should definitely document what you did and did not test, and why.