How do I explain to a student why departments that do similar things have seemingly different names?
I would say instead that it would be much more surprising if these departments all had the same names, particularly for relatively new and cross-disciplinary areas of work like in your example.

The domains of science are broad and overlapping, and there are many ways that the whole domain can end up being parsed into departments by different institutions, just like there are many different ways that the domain of colors are parsed into color names by different languages. 

Given that there are many reasonable possible clusterings and names, the actual determinants tend to be very contingent and historical.  Among these are:


Interdepartmental politics, including which part of a university wants to sponsor the new department, which faction of an old department wants to split away.
The viewpoint of the faculty forming the department
Popularity of subjects over time: small departments merge and large departments split.


There are many other possible causes as well.  Thus, the question is not: "Why are they different?" but "Why would you expect them to be the same?"