They make sense to be distinct when they are used distinctly.
On the English SE there was a question about the difference between 'nomenclature' and 'terminology': https://english.stackexchange.com/questions/20234/difference-between-terminology-and-nomenclature
The 2nd answer explains imho quite well the (tiny) difference: terminology is often a broader term while nomenclature less so and the better word to describe naming patterns for groups of thing like craters, stars, or comets. With this argument the question would need tagging 'terminology'.
Generally there are not many naming patterns in astronomy other than 'these objects take names from this mythological background and suggestions are decided by the IAU'. However these patterns are often asked or there are questions on the name of particular objects. So a separate tag for this does make sense - but it likely should be 'naming'. It's tag description could be like
naming: Questions about the names of actual celestial objects or naming conventions of a certain type of celestial objects. E.g. "how are comets named?", "what is the brightest nameless star"? etc.
Distinct from that, one then would keep the tag 'terminology' with a tag description possibly similar to
terminology: Questions about technical terms, differences in classification of objects. E.g. "what is the difference between an asteroid and a comet" or "what is a planet"?
Given the tiny but existing differences between terminology and nomenclature makes me think it falls in between these two suggested tags - and I would remove the tag altogether (or make it an alias of 'terminology').
One can argue that these two suggested remaining tags are still too similar, but with a proper distinction drawn similar to suggested, they can fulfill their role, even when sometimes the wrong one will be chosen initially.
