The definition of "species" found in the Mirriam-Webster Online dictionary is as follows:
1 a : KIND, SORT b : a class of individuals having common attributes and designated by a common name; specifically : a logical division of a genus or more comprehensive class
(1) : a category of biological classification ranking immediately below the genus or subgenus, comprising related organisms or populations potentially capable of interbreeding
The genus "Canis" includes a number of species, among them wolves, domestic dog, dingos, jackals, and coyotes.
Tiny dogs like Chihuahuas, and giant dogs like the wolfhounds or mastiffs, are POTENTIALLY capable of interbreeding. So they are members of the same species. However, such radically different breeds of dogs (or goats, or other domestic animals) are actually different subspecies.
The rank is genus; within genus, species; with species, subspecies. Subspecies occur both in nature and as a result of human domestication.
I am using the definition I am reading right here out of a 15 year old college Biology book.
There ARE alternative definitions that are less precise, I agree. But those are not the definition used in classification of species.