Programming

Rigor in definitions allows us to express a lot of complex things in a compact form. this allows us to treat "Cars" as something different than "Motorcycles" while both a motorized vehicles.

Meh. There's plenty of room in the gray zone between "car" and "motorcycle" where things like this or this can exist. The botanical world has worked very hard to create rigorous definitions of fruits and vegetables only to be completely ignored by cooks. The culinary world in general has done just fine for centuries without rigorously specifying whether taco's are sandwiches and cereal is a soup.

As long as it is generally understood what people mean by a word when they use it everything will be mostly fine. REST is an understood term, whether the inventor of the term meant something else by it is immaterial.