Let's start with Dances for Novices, as these are the ones most likely to need explaining. Karen teaches and calls a variety of dances that are suitable for all ages and mixed levels of experience. This is the sort of mix that suits what callers refer to as "One night stands," such as weddings, barn dances, youth group dances, etc.
It is useful — but not necessary — to move to the beat, and everyone can play. Popular dances like the "Virginia Reel," "Sasha," "The Broom (or Paddle) Dance," and circle mixers like "La Bastringue," work well here.
Square Dances are figure dances done in groups of 4 couples who stay together throughout a single dance. You've seen them on TV and in movies. You may even be of the generation that had them inflicted in P.E. classes during puberty. They are much more fun when you actually want to dance!
Also note: Unlike Modern Western Square dances that require months of lessons and funny outfits, Karen calls square dances compatible with people who have never tried it before! And the dress code is: Comfortable for exercise.
Contradances are much like square dances in that you do things with your partner, as well as another couple or two, each time through the dance. But in contradance, you move down a line of five or more couples instead of staying in a square of four couples.
For a good overview of contra dancing for people who have never seen it, here is an article by a friend: HANDS FOUR: "What Is Contra Dance?"
English Country Dancing is somewhat like what you see in Jane Austen movies; more stately and precise. In general, this is the ancestral form to modern square dancing and contra dancing. It can be lively and complex, or stately and elegant. English might even be in 3/4 time, waltzing through the figures.