The relationship between Hades and Pluto is a bit more complicated than the simple association between a Greek god and its Roman counterpart. The ancient Greeks weren't too fond of Hades – the Unseen - so much so, that they even avoided mentioning his name – and for the world, I can't imagine why. Well, he was god of the Underworld and spent his time among the dead, but still, there's nothing spooky or ruthless about Hades, quite to the contrary, he was a just and reliable ruler, and got a bad name just because he wasn't in the habit of allowing people to leave his kingdom and return to earth... which, putting things into perspective, seems fair enough to me.
Still, the Greeks always fancied the glitzy Zeus or Poseidon against the reliable and just Hades, so the god of the dead didn't even have myths of his own. He's only mentioned in the story of how Persephone was kidnapped – which belongs to the cycle of legends related to Demeter – and in another story in which Herakles descends in the Inferno, wounding Hades in the process. Of course, this second story belongs to the cycle of legends related to Herakles – leaving poor Hades with very little to say for himself. He does make some cameo appearances in the stories that involve all gods, like the battle against the titans – but those don't really count, do they?
Still, every now and then the Greeks had to mention Hades, and when this happened, they preferred to use a euphemism instead of his real name, and one of their favorites was Pluton – meaning “the rich” - which later was Latinized and ended up as the Pluto we know today. Now, Hades / Pluto was in a way the god of riches, especially those that came from underground – silver, gold and gems. Also, during the winter, the seeds of plants, being underground themselves, were in the care of Hades and especially of his wife, Persephone / Prosepina. For these reasons, both these gods were often represented with a cornucopia, symbol of abundance and riches, and, in the classical tradition, also a symbol of Demeter, Persephone's mother (family ties... nothing like them, in myth and in life).
Now, Pluto the rich should not be mixed with Ploutos, god of riches... oh, well, the similarities are striking, so let's talk a bit about this Ploutos, even if he doesn't technically belong here. He was the son of Demeter, and initially a companion of his mother and sister (the sister being Persephone, in case you've lost track of relatives). As society evolved, wealth increased, and Ploutos gained the right to become a proper god, not just a mere companion. But responsibility came at a price, and Zeus blinded him, to make sure he didn't see which humans were good and which ones were bad – and thus riches were distributed to all, randomly, and not based on their merits. See? Nothing to do with the just Hades / Pluto, who distributed rewards and punishments according to the merits and deeds done in life.
Before becoming Pluto, the Latin god of the dead was Dis Pater – father of all riches – an agrarian deity. There was also an Etruscan god named Orcus, originally ruler of the underworld, who was later on demoted to punisher of people who broke their oaths. Accidentally, Orcus may be the root which led to the word orc.