I would tend to agree with Kate that it depends. Personally I haven't seen a "standard or common term" in testing literature that only describes changes to new functionality or to existing functionality.
The industry tends to give formal labels or terms to test techniques and approaches based on what we are trying to discover or measure. So a term like regression testing might be considered an activity based technique, functional testing might be considered a coverage based technique, etc. It seems like the items you've listed you are worried about risks based tests (finding potential problems) associated with new features, changes to existing features, etc.
If you are concerned about sounding credible when referring to these things, my advice is: be simple and direct. For example I might say:
- I'm testing bug fixes (or trying to disprove bug fixes)
- I'm testing new features
- I'm testing changes to existing features
- I'm regression testing x, y, z features
It doesn't matter so much what label you use, as long as your team and the people you work with understand what you are doing and/or trust you to do the job.