Glad I'm not the only one with this question. I originally posed it in the general reefing section and bumped it, but no one seemed to know there, so moved it here...
I started thinking about it when I was telling my mom about all the different zoo color variations (I think I know the answer to my first question, not different species). She is into gardening, and I was thinking the way reefers trade zoo frags for new colors is much like how avid horticulturalists trade plumeria and rose cuttings of new colors, sometimes those are pretty wild also (she got all excited and wanted me to set up a new SW tank for her, but I refused after I saw how she never changed the water in the FW planted tank I set up for her years ago...). Except the difference with the horticulturalists is that they produce new strains through sexual reproduction. This is how you get really bizarre looking roses that are jet black with red and white streaks and curly edges, you never see this in Nature.
With reef tanks, I know spawning sometimes happens under good conditions in a hobbyists tank, but it was my understanding that raising polyps from their planktonic forms was close to impossible in the trade, and so that the corals we see in the trade are either collected or gotten from vegetative propagation, i.e. the fragging we all do. This is asexual reproduction; = no genetic recombination.
On the lighting, it's also my understanding that different lights with different wavelengths will excite different types of zooxanthelae in various corals, which causes this color change effect. Also, I know zooxanthelae can sometimes migrate from one coral to another, for example, when a coral bleaches and then comes back another color, or when two colors of frogspawn grow together, but the stronger zooanthelae take over both. I just would think zoos are more complicated than that.... it's not just 2 or 3 colors that they come in, but literally hundreds of different exotic combos that almost look painted on. Every time I think I've seen it all, I look in someone's gallery and see another "Wow, I gotta get me some of that!".