In the software maintenance process, after a new version is built, there comes software maintenance testing.
In extent of software maintenance testing, it is done;
Please fill in the blanks, what is X and Y Testing?
It depends.
For new features and changes to existing features, exactly how you label the testing that's done will depend on a number of factors, including:
In my experience, it usually all get labeled in the catch-all of "functional testing" and precisely how much and how detailed depends on the change and where in the process the new build is made available.
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:
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.
Primarily they can be
X --> Sanity Testing
Y --> Regression Testing
There can be other values also for Y such as Integration testing or System testing
