The easiest way to describe what each one is as:
kH Carbonate hardness- is the levels of calcium and other soft deposits in the water
gH general hardness - is the levels of other heavy compounds or metals in the water including silicates.
the way i understand this is that kH is a buffer which controls your pH so if your kH is high your pH will generally be high too. And then gH is a buffer for your kH which in turn determins how stable your kH is. CONFUSING AS HELL!!! but all this is reletive to how stable your pH is.
For example you can have a tank at ph 6.5 with a kH of 4 degs, but your gH is around 18. This will make your pH unstable because in theory your gH levels can raise your kH levels over time, this is why i use R.O water, because its got nothing in it and you can build the composition of the water yourself.