The definition isn't fuzzy, we define a brown dwarf as an object that has undergone deuterium fusion.

The fuzziness is in the physical properties needed to achieve that. 13 Jupiter masses is generally the threshold where deuterium fusion starts, but that can vary: a brown dwarf composed of only primordial H and He would need a bit more, while one with some heavier elements from previous generations of stars will be denser and need slightly less. Rotation speed also matters: a faster rotator will experience centrifugal force and thus have less interior pressure.

And there is fuzziness in what we can observe, so sometimes we're not sure if an object is a brown dwarf. We may not know its exact mass and composition, and we might not be able to tell if it's radiating energy from deuterium fusion, or just from gravitational compression, or (in a binary system) if it's just reflecting light from its companion star.