No, there actually is a "gold standard" for defining the differences between breeds or sub-species versus species, genera and families.
Breeds (i.e., dogs), varieties (plants) or "races" (humans) can and do readily interbreed.
Sub-species also interbreed, but not so readily or successfully.
We think today that Neanderthals were a sub-species of humans.
Different species of the same genus don't normally interbreed in the wild, though sometimes can be forced in captivity.
A typical example is horse and donkey species producing sterile mule offspring.
Different genera of the same family usually cannot successfully interbreed, even when forced, for example, African and Indian Elephants.
Bottom line: it's the degree of difficulty in interbreeding which helps tell biologists how closely related are two different populations.