What is a good word for the identifying characteristics of something?

Solution 1:

When I worked in scientific research, we called these distinction sets (for a group) or comparators (for the individual parameters).

You might also call them distinguishing features or points of differentiation/distinction.

Solution 2:

The classic term in our “problem space” is probably Roman Jakobson’s distinctive feature, one of a small set of acoustic or articulatory features which collectively distinguish the phonemes within any language’s phonological system.

The concept has been usefully extended to other disciplines — Lévi-Strauss, for instance, employed it fundamentally in the structural study of kinship systems and mythological corpora. But linguists may be vexed if you employ the term for features which are not privatively (that is, present/absent, +/−, binary) defined.

For instance: “Hair color (white, blond, red, brown, black) has too many choices and would not be a distinctive feature. But you could pick one distinctive feature—say, “fair+/−” — and have two choices: Blonde (fair+) and Brunette (fair−). Two features, “fair+/−”, “color+/−” would allow you to distinguish four colors: Blond (fair+,color−), Red (fair+,color+), Brown(fair−,color+) and Black(fair−,color−). And so forth.