I believe they can be used separately, and the questions I have posted so far indicate their distinctions.
For example, I asked "Placing incoming college freshmen: basic algebra, pre-calc, calc", and this is truly an assessment question: how do we assess the abilities of incoming students and place them into courses? Implicitly, I suppose this is a grading question: how do I grade a placement test appropriately to get meaningful results? But ultimately, this question is more about assessing abilities.
Contrast that with some questions under the "grading" tag, like "Grading problems that nobody solved" and "How to standardize grading across several sections of a course?". I believe these are also questions about assessing abilities, but ultimately they are more about the process of grading assignments/tests.
So, I think these should be separate tags. (If others feel differently, that is fine.) But I'd like to make public note of this distinction, making others aware of the "assessment" tag so that you can post some appropriate questions under it and make the differences more pronounced.