A great example of why taxonomy matters can be illustrated with this example: Are objects orbiting brown dwarfs "moons" or "planets"?
The answer to this question is much more complicated and controversial than it might seem, but it is very much related to the need to have useful definitions for sub-stellar bodies.
The official IAU definition for a brown dwarf is a sub-stellar body that exceeds the deuterium burning (DB) limit no matter the mechanism of formation. Well that seems ok ... right? Sure - definitions are not "right" or "wrong" they are "useful" to varying degrees. The DB limit is convenient because it is only based upon mass, but it is not useful to answer the question of what we should call objects orbiting brown dwarfs.
The concept of Brown dwarfs was proposed in the 1960's by Kumar, who determined that the star formation process (gas collapse) could produce bodies too small to begin core hydrogen fusion. He referred to these objects as "black dwarfs" and later on they became "brown dwarfs".
When I was growing up the the 1980's Jupiter was sometimes referred to as a "failed star". However, this is not the case. Jupiter did not form by a stellar gas collapse process. Instead it formed within a protoplanetary disk. The preferred theory today is the "core accretion" theory in which Jupiter began by building a rock/ice core that upon reaching a mass somewhere between 5-10 Earth masses began to accrete its massive hydrogen envelope. There are other proposed mechanisms and stages of the mechanism such as disk instability and pebble accretion. The important thing is that a body formed in a protoplanetary disk will have heavy element (elements more massive than Helium) enrichment relative to the parent star. And such is the case with Jupiter and Saturn. Both have heavy element mass percentages well above the Sun's.
The IAU's adoption of 13 Jupiter masses to distinguish brown dwarfs from giant planets is problematic for a number of reasons:
1. Observations have shown that gas collapse mechanisms can form objects as small as ~4 Jupiter masses.
2. It is possible for core accretion or disk instability to form objects in a protoplanetary disk that exceed the 13 Jupiter masses
3. Plots of Mass-radius relationships (used to characterize exoplanet characteristics) show no feature that would indicate there is any significance to deuterium burning.
4. Deuterium burning is a short lived stage that has negligible impact on object formation and evolution.
5. As noted above, objects that form by gas collapse do not have the heavy metal enrichment and core that objects formed in a protoplanetary disk have. Gas collapse products have a hydrogen core.
Items 1&2 result in an "overlapping mass regime" for brown dwarfs and giant planets. What this means is that there is no mass boundary (including DB) that provides a way to distinguish a giant planet from a brown dwarf. Between 4 and at least 10 to possibly 42 Jupiter masses the body may have formed by gas collapse or it may have formed in a protoplanetary disk.
Items 3&4 illustrate that DB is not a meaningful aspect of giant planets and brown dwarfs - so it does not make a useful criteria that creates more understanding in our classification system.
Item 5 is important because it illustrates that a brown dwarf and a giant planet - even if the same mass - do not have the same structure, history, and composition.
So what is the solution? If we are trying to have definitions that are meaningful then this should be the definition for a brown dwarf:
a gaseous, sub-stellar mass body, formed by star-like gas collapse mechanisms, with insufficient mass to enable core hydrogen fusion.
The mass range for brown dwarfs would then be 4 to ~60 Jupiter masses. But some objects in the lower end of that mass range would be giant planets.
And the original question: Are objects orbiting brown dwarfs moons or planets? The answer is that since brown dwarfs form like stars the planetary mass bodies orbiting brown dwarfs are planets ... or dwarf planets if they do not dominate their orbit.
As can be seen - to get to that answer requires a lot of consideration of science observation and theory. And so it is with the definition of "planet". The IAU did have a good reason to look at the problem, but the solution they came to was not as useful as it needs to be.