Orcus was a god of the underworld, punisher of broken oaths in Roman mythology. He was more equivalent to the Roman Pluto than to the Greek Hades. He was portrayed in paintings in Etruscan tombs as a hairy, bearded giant. Orcus is also said to have inspired orcs, a race of pig-like men who frequently appear in modern fantasy. This is apparent in the series as Orcus appears as a grotesque pig-headed creature.
"Origin: Italy. A malevolent Roman god. He is one of the gods of the underworld, and has a pig's head and bat wings. He's daring but violent, and will massacre enemy troops in order to eat them. He sometimes appears as a giant dragon with fangs of iron."
"I will not stop until I have sipped on a chalice of your blood!"
—Orcus before engaging the player
Since Orcus is the same person as Horkos in this canon, their battles are also similar. Orcus uses the same attack pattern and has the same weaknesses, but has more resistances. Orcus retains all of Horkos' unique moveset but some moves now have upgrades. Chomp is now changed to Taking a Bite but still retains it's properties of being a Life Drain-esque attack. Grocery Run still summons a single Katakirauwa although now each Katakirauwa summoned is at level 46.
Orcus typically has a "pig" design, but this was given to Horkos, Orcus' Grecian counterpart, due to plot related reasons in Shin Megami Tensei: Strange Journey. As a result, Orcus exhibits a new redesign in this game but in all other games, Orcus retains some resemblance of a pig in one form or another.