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The common terms used to refer to the Greek/Roman god of death are Hades or Pluto, yet in the Aeneid, the god of death is commonly referred to as Dīs. Further, the realm of Hades (the Underworld, which I've also heard referred to as Hades) is referred to as Orcus, but I've read that Orcus was a punisher of broken oaths.
Where did these differences come from?
As Andrew Johnson has noted, Dis is a shortening of Dis Pater, the principle god of the dead and the underworld for the Romans. Unlike Pluto, Dis Pater was a native god, more or less original to the Italian peninsula (in as much as any mythological figure is native anywhere), and specifically the Italic peoples (also known as the Latins). Orcus was, some suggest, an import from a nearer neighbour, the Etruscans. Pluto was most likely an importation from the Greek Plouton, an appellation of Hades referring to his association with the "wealth of the Earth" (minerals).
I understand that the Romans mostly associated the figure of Pluto with this wealth-related aspect, though they held him as a chthonic (underworld) god. Dis was the more benevolent underworld god (hence, I believe, his being identified as a father figure). Orcus was the vengeful side of the lord of the dead, punishing especially those who broke oaths. These are all gods of the dead, rather than death; the personification of death was Mors, the equivalent of the Greek Thanatos.
Now, the underworld itself, the realm of the dead, was often referred to - by both Greek and Roman tradition - by the name(s) of its ruler(s). Orcus's name may have actually started that way, as it could be linked to Greek roots referring to enclosure, containment or restraint. However, Romans would happily use quite a range of names, including Orcus, to refer to the realm of the dead.
It is worth noting that Roman mythology is not a coherent whole. Not only did they apply Interpretatio Romana to foreign gods and myths, especially of people they considered beneath them, but they also imported mythic elements and figures of other cultures (primarily but not only the Greeks, to whom they applied a mixture of importation and interpretation) wholesale and worked them into their own syncretic hodge-podge. It is often unclear whether they considered Pluto and Dis different aspects of one god, or two gods with overlapping provinces, and it's often unclear to what extent such a question would even matter to them.
Dis comes from the god Dis Pater, the chthonic deity of riches and fertility. Orcus is as you say, a punisher of those who swear false oaths.
Dis Pater was often shortened to Dis. It has sense become an alternate name for the Underworld(i.e. Erebus, Hades, Pluto), or a part of it. The same with Orcus. Entomology says his name meant land of the dead.
The god of death is often said to be Hades/Pluto, but is actually Thanatos/Mors.
Simplified, Dis is a name for the Underworld. Orcus means Underworld. The Underworld takes its name from the ruler. Thanatos is confused with Hades. Hope this helped.
