It seems that interbreeding between wolves and dogs was deemed possible in Roman culture at least at the time of Pliny the Elder (I cent. CE.) But so was the idea of interbreeding between dogs and tigers.
I was curious and went to Pliny's Naturalis Historia.
It happens to have separate chapters for wolves and dogs. The latter happens to mention wolves and... tigers. It gets interesting.
It says that Indians interbred tigers and dogs (!):
E tigribus eos indi volunt concipi (Plin. Nat. 8.61) The Indians raise a breed between the dog and the tiger (Bostock, 1855)
and it goes to explain how they did it.
Right after that, it also says that the Gauls did the same (interbreeding, apparently) with wolves and dogs:
Hoc idem e lupis galli, quorum greges suum quisque ductorem e canibus et ducem habent The Gauls do the same with the wolf and the dog, and their packs of hounds have, each of them, one of these dogs, which acts as their guide and leader
The XIX century translator/editor adds a footnote favoring the plausibility of this, as if writing for a skeptic reader:
The dog is capable of generating with the wolf; and as what is termed the shepherd's dog much resembles the wolf, Cuvier conceives it not impossible, that it may have originated from this mixture
In contrast, the previous footnote discredits and tries to explain the statement about the interbreeding of dogs and tigers:
This practice is mentioned by Aristotle, Hist. Anim. B. viii. c. 33, and Diodorus Siculus, B. xvii. But Cuvier informs us, that neither the tiger nor the panther are capable of generating with the dog; he supposes that the account was invented to enhance the value of the spotted or striped dogs, which were brought from India
Regarding the question on practical or mythical distinction between them, the chapter of Naturalis Historia on wolves talks about something very similar to werewolves, discrediting them as a myth. In turn, there is no mention of men turning into dogs in the relevant chapters:
Homines in lupos verti rursusque restitui sibi falsum esse confidenter existimare debemus aut credere omnia quae fabulosa tot saeculis conperimus (Plin. Nat. 8.34) That men have been turned into wolves, and again restored to their original form, we must confidently look upon as untrue, unless, indeed, we are ready to believe all the tales, which, for so many ages, have been found to be fabulous
Wolves are also said to have a noxious influence in the eye:
Sed in italia quoque creditur luporum visus esse noxius vocemque homini, quem priores contemplentur In Italy also it is believed that there is a noxious influence in the eye of a wolf; it is supposed that it will instantly take away the voice of a man, if it is the first to see him