Here’s what I was told in college biology, kinda basic and oversimplified:
Animals are considered a different species if two specimens that do not normally mate are cross bred and do not produce viable reproductive offspring.
A mule, a cross between a horse and a donkey, is sterile and cannot produce reproductive offspring.
Dogs and wolves can produce reproductive offspring because dogs are essentially wolves of a different race.
Black, white and Asian humans obviously produce reproductive offspring, so we are a single species.......
I expect the amount of DNA we share would support this taxonomy. About as good as any. So to summarize, it’s the ability to have babies togeter that makes a species. I’d say your wolves and dogs example means there is some correction to do to the species taxonomy based on this rule though. Even wolves come in diffferent species: the dire wolf (Canis dirus), the gray wolf (Canis lupus) and the coyote (Canis latrans). One additional species, the domestic dog ...etc etc.