The Kelvin rating... (k) is the color spectrum of the bulb. 10,000k is more yellowish/red/white while 12-15k is more whiteish blue and 20k is blue but not actinic.
Most people choose their halide color for aesthetics, growth, and coral colors (florescence). For example,
10k - makes oranges, yellows, reds, green corals colors "pop" while also providing substantial growth.
now - I'm a little colorblind, so I really prefer the 10k look to other spectrums... but the 12k-14k spectrum is a lot more "white" and makes the corals colors pop as well, including the added benefit of florescence.
20k halides make all capable corals floresce, but will also make blue, purple, and some greens look darker or not floresce as much as they would if under 12-14k's.
Your type of ballast also determines what exact color the bulb produces. A 12k bulb on a certain ballast could look more yellow or more blue depending on the ballast.