I omitted this phylum owing to the fact we have no true varmints to speak of where I live. This, however, is no excuse.
Similar in many respects to a critter, a varmint is typically mammalian, larger than a breadbox, and smaller - thank goodness - than a Great Dane. While critters are a nuisance, varmints are specifically predatory. Coyotes, bobcats, IRS agents, wolves, and hyaenas are varmints. Varmints are the type of animal that will sneak onto your ranch and steal one of your dogies, or run off with one of your chickens in the night while you shake your fist uselessly from the bedroom window.
As I said, we have very few varmints in our area, and those we do have, are only varmints part-time. We have a little fox, but until the day he gets one of my chickens or the neighbor's pet morkie, he's only a critter, not a varmint. Years ago, some animals - either raccoons or possums - got into the coop and ate my chickens. At the time they were varmints, but they haven't done so in a while, and they've been relegated back to critters.
Becoming a varmint is a crime of opportunity for many critters, and just being a varmint justifies being shot on sight. Seeing a varmint and saying, "Poor little critter," is the equivalent of saying, "Bless his heart."
The menace of varmints as opposed to critters and pests is evidenced by the fact there actually is a varmint rifle, but there is no such thing as a critter rifle. The concept of a pest rifle doesn't even make sense.
The relative lack of varmints in the modern world has led to a new kind of menace. For hundreds of thousands of years, humans went varmint hunting, which not only helped reduce the varmint population, it provided a constructive outlet for violent tendencies that would otherwise do harm. Now, genuine varmints have largely died out, but the taste for the hunt dies more slowly. If you can believe it, full grown men sometimes patrol gated neighborhoods by night, armed and eager.