what is “a group of living things that can interbreed and produce full interfertile offspring”?
Based on the biological species concept, you're referring to two different species that experience ecological isolation (also called "habitat isolation") as a prezygotic reproductive isolating mechanism. 

See here for a simple explanation of various concepts regarding species.

This, of course, is just one of the many reasons (see here for more) why we have multiple species concepts. Some might argue that these organisms are the same species based on their ability to produce interfertile offspring. If said researcher wanted to do so, they would define these organisms using a different concept. 

Recognize that “species” is an artificial construct to allow conceptualization and organization of an incredibly complex, dynamic, and otherwise continuously variable genetic world. 

We have not found a perfect way to "cut up" the world neatly/consistently into describable and functionally useful units, and --in fact -- we likely never will. Why? Because the lives of these organisms do not care about our cataloging and description systems -- these concepts are strictly for humankind to functionally relate to and react to their presence. The concept chosen almost inherently relies on the underlying motivation of the describer for naming the organism in the first place.