Was the Greek Herakles the same hero that the Romans worshiped as Hercules? The answer devolves from Yes to Maybe and then No.
The differences between the Greek and Roman gods and goddesses have become so blurred over the centuries that it is sometimes difficult to tell one from the other. Instead of comparing the Greek and Roman deities, many books and mythology web sites use the term "equivalent" as if the Greek and Roman deities were identical. There are numerous popular translations of ancient Greek literature in which the Greek gods and goddesses are never called by their Greek names! Zeus becomes Jove, Ares becomes Mars and Herakles becomes Hercules etc. The translators substitute the Roman names for the Greek names and no one seems to notice or care. The result has been that many people are convinced that the ancient Romans did not have an original religion at all and that the essence of their spiritual life was nothing more than a revival of the ancient Greek religion with the addition of a few Roman flourishes and new Latin names for the gods and goddesses. Both religions have been relegated to the category of myth and today it would seem that to quibble over their unique differences is unimportant. The ancient religions of Greece and Rome were not myths to their worshipers... the real myth is that we equate these two religions so willingly and completely.
One of the main problems with the heritage of the Roman deities is that there is no Theogony to document their interconnections. To refresh your memory, Theogony is a poem written by the Greek poet Hesiod in the mid-seventh century BCE in which he methodically lists the Greek gods and goddesses, their parents, their descendants, their role in the cosmos and, most importantly, their true names and pseudonyms. Sadly, our knowledge of the ancient Roman religion does not include a definitive text such as Theogony to delineate their gods and goddesses. I believe that this gap in our