The definition is fuzzy because the concept is fuzzy! Even something that we in every day life see as settled such as a species is not always clear-cut. Cat or dog? That's usually easy. Member of a species yes or no? Not so easy, and in some cases subject to considerable debate and even then unresolved.
For instance:
https://en.wikipedia.org/wiki/Species_complex
And:
https://en.wikipedia.org/wiki/Ring_species
Boundaries are hard, just like naming things.
It is misconception that hair and nails continue to grow. What happens is the that kind and soft tissues dehydrate and shrink and the hairs and whiskers stick out more. Growth stops soon after oxygen and nutrients stop being delivered.
Just like geology doesn't have a great definition for their subject of study (the earth). They have a definition that works really well, but because they only have one example, the definition ain't stress tested.
Slightly less silly: it took the discovery of lots more bodies inside and outside the solar system (dwarf planets here, exoplanets elsewhere) for astronomers to really nail down the definition of planet.
Autopoiesis and Cognition: The Realization of the Living (1980)
https://en.wikipedia.org/wiki/Autopoiesis_and_Cognition:_The...
Unfortunately out of print.
The result is a landscape of fuzzy definitions mostly centered around that last one.