Roman depiction of Seth-Typhon from Gifford, D.J. (1979). Iconographical notes towards a definition of the medieval fool. In P.V.A. Williams (ed.), The fool and the trickster: Studies in honor of Enid Welsford (pp. 18-35). United Kingdom: U.S. Brewer.
Technically, the word Typhonianism refers to a particular era in the history of Seth worship that began during the Late Period (circa 664 BCE) and that ended in Greco-Roman times (circa 395 CE). This is when Egypt lost its native rule to the Persians, then to the Greeks, and then to the Romans; it would not enjoy self-rule again until the twentieth century. As the Divine Foreigner, Seth became a convenient scapegoat for the fact that Egypt was now ruled by outlanders. For thousands of years prior (circa 3200 – 664 BCE), He had been acknowledged as a God who might be unruly and intimidating, but who was no less essential to the cosmic order of things than the rest of His divine family. But as Egyptian xenophobia grew in classical antiquity, so did the concept of Seth as a completely malevolent force. This is when He was first identified with the Greek monster Typhon by Herodotus, which led Him to become something of a “proto-satanic” figure. The worship of Seth continued, but it was no longer endorsed by kings or priesthoods; now it was the province of lone sorcerers and witches, who had to engage the Red Lord in secret. Since the Egyptians of this period were quick to kill anyone or anything that they regarded as being too Seth-like (including red-haired animals and people), worshiping Big Red had become very dangerous indeed.
Another thing that happened during this period was the development of the Greek Magical Papyri, which are a collection of spells that blend Egyptian, Greek, and Judaic influences. Quite a few of these spells include incantations to a figure called Typhon, but this figure is very different from the Typhon of Greek mythology. The latter is simply a chaos monster with no positive qualities whatsoever, and which was identified primarily with serpents. The Typhon of the papyri, however, is associated with donkeys, the color red, and the constellation Ursa Major. He is also addressed as a misunderstood hero who keeps the universe in constant motion by (1) slaying Osiris and (2) slaying “the unseen serpent” (i.e., the Backward Face). Most interestingly, He is engaged as the “God of Gods,” a Divinity who is more powerful than any other, and whose actions are completely necessary for the good of the world. It is very clear from all this that the Typhon of the Greek Magical Papyri is actually Seth in a later guise, and that these Typhonian spells are merely Hellenized versions of earlier Sethian practices.
I prefer to use the word Typhonianism for my religion because I find that using Typhonian yields the most useful results about my God and His lore in an academic literature search. (If you search for Sethian, you’ll more often get results pertaining to Gnosticism, which is a whole different beast.) But I also prefer this term because I’m partial to the era of Seth’s history when the Greek Magical Papyri were produced. After living in Texas for such a large chunk of my life (and during the Bush Administration, no less), I can really identify with the idea of having to worship Seth-Typhon in secret, and of knowing that I am really doing something good (even if the rest of the world thinks it is “evil”). Perhaps that will strike some people as being melodramatic, but it is what it is.