They are completely different, unrelated fruits. Brambles aka blackberries grow on a thorny bush, wild as a weed, all around London and whole Europe, ripening in autumn, which is why it makes sense you won't see many of them in Argentina. Mulberries grow on a big tree with no thorns. So far, I have only seen then in warmer parts of Slovakia and Hungary. Different climate as well. Very specific to Europe, don't know about America.
By the way, what would be the local Argentine version of edible weed fruit? I mean, berries that grow everywhere, wild, for everyone to eat for free? I've seen quite a few fruit-bearing plants in Reserva Ecologica, but didn't dare to taste, at least not without asking first...