I'm certainly NOT the best person to answer this. But I will try. Ask others, Jim Perry and Jake Pehrson could elaborate. The K rating is a Kelvin rating. Basically this tells you what spectrum of light you are dealing with. Think of it this way, is the light bright white, is it red like plant lights, is it blue, is it green, is it a black light? Basically the K rating tells you the spectrum you are dealing with.
What do corals need? Once again, I'm not the best at this. I like 6500 K for most applications because it is a soft white/blue light. I'm also a fan of adding blue or actinic lighting. My view is that bright white is ideal for 8 hours a day, and you can never have too much actinic lighting. I would run my blue lights (I think they are 4500K) for atleast 12 hours per day.
Hope this helps,
Adam