We don't need a source to explain to us the difference. We have enough ancient evidence and mentions of both men to rest easy in the knowledge that they were, in fact, different human beings. They weren't even the same age. People with the same name is extremely common in the ancient world. Athens, compared to Rome, had a luxury of different names. In Rome, at any given time there were probably three dozen Lucius Cornelius or Marcus Claudius running around.

Thucydides the Historian tells us himself in his history that he is the son of Olorus, from the Attic deme (neighborhood) of Halimous. He tells us about his unfortunate involvement in the disaster at Amphipolis during the early stages of the war, which caused the Athenian people to ostracize him. His family had connections to Thrace, and in fact he tells us that he owned property there (5.26). His father, Olorus, was connected with the Thracian ruling class, as per Herodotos (6.39).

The other Thucydides was a completely different person. Though he did not write about himself, we have his basic details from other ancient writers. He was the son of Melesias, and his home deme was Alopeke. He involvement with the "conservatives" at Athens in opposition to Perikles is well known and mentioned in contemporary sources like Psuedo-Aristotle's "Old Oligarch" and Aristophanes "Wasps."