What's in a name?
Permafrost is a word used to describe any soil (or rock) that remains frozen indefinitely. As an aside, it's not a very good word because it suggests that the frozen soil is permanently frozen (and may inadvertently convey a sense that it is not subject to thawing). Permafrost in Fairbanks is only a few tenths of a degree below freezing. Not only can it thaw, but it can be said that Fairbanks permafrost is downright hot and it wants to thaw.
In practical terms, permafrost comes in two basic flavors. One flavor is called "epigenetic" and the other, "syngenetic." Epigenetic permafrost is soil that was already pretty much in-place when it froze. Think of a thick deposit of sand freezing from the top down over many thousands (or millions) of years. The sand was frozen after it was already deposited. The other kind of permafrost froze as it was being deposited, layer by layer. The soil (and sometimes other things like sticks and twigs and the occasional unfortunate Ice Age animal) froze along with water that washed it into place, which then became ground ice.
The name "SYNGEN" (pronounced "sin-JEN") is a shortened version of the word "syngenetic," which, as implied above is a term used by permafrost enthusiasts (who probably should get out more), to describe a very special kind of permafrost notorious for its unusually high frozen water content and for the large deposits of clear ground ice it often conceals.
Syngenetic permafrost is also infamous to many Interior Alaskan homeowners as well as Alaskan placer gold miners for the hazards it poses to building constuctin and excavation stability. It is also famous to many University of Alaska Fairbanks Museum-goers for the frozen remains of now-extinct Ice Age animals it sometimes preserves (seriously . . . think 10,000 year old Steppe Bison stew).