By characterizing feature, I'm referring to an attribute of something that uniquely identifies it. Is there a single word that describes such a feature? Characterizing and distinguishing come to my mind, but I feel as if there are a lot more terms for this that I'm missing.
a distinguishing trait, quality, or property
- the characteristics of this breed of dog
The term in logic is definiens—that which distinguishes an entity from all other entities. The term is traditionally employed to speak of predicates—verbal or symbolic expressions—but there is no reason you cannot extend it to the properties which the expressions signify.
But this is unlikely to be a single "feature" or "characteristic", since an entity may share such properties with other entities: it is more often a set of properties which is unique to the individual. In this case we may speak either of the set as the definiens or of the individual properties as plural definientia, each distinguishing the entity from some but not all other entities.
I imagine there are different words depending on context, area of study. In marketing, the nearest is probably USP.
a feature of a product that makes it different from and better than other similar products and that can be emphasized in advertisements for the product
In medicine or biology, I think they are referred to as defining or diagnostic features.
In bird watching these are usually called "distinguishing" or "distinctive" features. You find them both used for example on this page of the Audubon Society site on how to identify birds. https://www.audubon.org/content/how-identify-birds
endemic (to) -
- natural to or characteristic of a specific people or place; native; indigenous:
endemic folkways; countries where high unemployment is endemic.
- belonging exclusively or confined to a particular place:
a fever endemic to the tropics.
of the nature of or serving as a type or representative specimen.
conforming to a particular type.