It's come to my attention that I'm, well, not really speaking English anymore. I've gotten so immersed in bee culture that I forget not everyone knows the lingo. So here's some, and I'll be adding more as I think to:
A nuc is a nucleus colony of bees, consisting of 4-5 frames (the ones we bought were five-frame nucs) of drawn honeycomb, a couple thousand worker bees, maybe a few drones, and one mated, laying queen. It's like a mini-colony.
You put that into a new hive (the structure), which they then make home and build out into what you hope becomes a strong, full-sized colony.
Colony, by the way, is the group/family of bees living in one hive.
So we've got three colonies in three hives: Winnie the Pooh, Fish, and Wonderland.
People use different size boxes for the brood boxes & honey supers. What we've chosen is to use "deeps" for brood boxes, which is where the bees really live & the queen lays all her eggs. They make & store honey there too, but that honey is left for them to eat. It's also where they store nectar & pollen, and care for the eggs/larvae/pupae and do most of their work inside the hive.
We use "mediums" (a few inches shallower than deeps - 3 mediums ends up the same height as 2 deeps) as honey supers. Once the deeps are filled out, the supers go on top for the bees to fill with just honey, and that's the honey we can take for us to use, eat, and sell. Some people use "shallows" (2" shallower than mediums) for their hives, but we don't bother. It's a matter of what you're comfortable lifting when they're full.
To harvest, we'll be borrowing or buying an extractor. The frames of honey-filled comb are put in after slicing off the beeswax caps from the comb (when the honey is ready, the bees cap it over with wax to keep it stored), and slowly spun so the centrifugal force removes the honey. Then it's put through a sieve or cheesecloth to get out any bits you don't want (we'll be using one that's not TOO tightly woven so it doesn't remove pollen) and jarred.
There you go!