Why the Covenant are from the main Covenant.

Games Other Halo
1

In the E3 campaign demo/trailer, Master Chief runs into the Covenant, which consists of an elite, a jackel, and two grunts. One of the grunts does something very interesting and says, “The demon!” Not only does the sound of his voice show of the fact that the grunts are still high-pitched clowns, but that they have connections to the rest of the Covenant in some way shape or form.
Although this is just an educated guess, they could have recently split from the main Covenant fleets or the grunts could have just came up with this nickname in the short time since their first contact, these two reasons are unlikely, but possible.

tldr, Covenant are probably still connect to the main Covenant because of what the grunt says.

2

Or you can wait and see what the Trilogy by Karen pumps out. Glasslands is the first of those three, and it mentions Infinity prominently near the end.

3

The Human-Covenant War lasted for almost 30 years, during which Spartans were referred to as demons by most Covenant Species. Even after 4 years, that’s a habit that doesn’t die easily.

4

Calling SPARTANS and other powerful adverseries “Demons” has probably become memetic for the Covenant. They’be been fighting thse enemies for 30 years, they’ve received terrible wounds and losses during confrontations with them, and they may still be religiously/politically inclined to fight them, as Toa Freak elegant said, “even after 4 years, that’s a habit that doesn’t die easily”.