I often use an article that appeared in Vivarium magazine in the mid 90's as a reference. I don't have the volume and issue number handy, but can post it if needed.
Unfortunatly cal kings have not had the benefit of more or less standardized names to the extent of cornsnakes for instance. Additionally, whereas the vast majority of corn morphs are simple recessive, many of those in cal kings behave somewhat differently, and have much more to do with pattern than color.
The common cal king is not actually black and white, it's black and cream to yellow, with the light bands being fairly narrow.
Desert phase is stark white and black. Number wise, this one is more common I wouldn't doubt, because it is normally preferred over the "normal" cal king.
This would be considered a common or normal cal king:
50/50 refers to a widening of the white bands. When the term was first used, it denoted a specimen in which the width of the black and white bands were more or less equal. As selective breeding continued, there became 60/40's, and so on, but this is little more than estimating really, and many of these were still called 50/50.
At some undetermined point, the white bands get so wide a 50/50 becomes a high white.
The exact definitions of the different terms will vary depending on who you ask and how long they have been involved in the hobby.
For instance, a coastal phase, which is brown instead of black, was once known as chocolate, but chocolate was first used for melanistics.
This would be a striped coastal:
Click for a larger pic.
Banana was originally used to describe a pattern, it was also called "crazy pattern" but the name didn't stick. Lately many relate the banana name to color and apply it to high yellow individuals.
This is an example of the pattern that was called banana at first.
I tend to agree with the use of it to describe color, as that makes more sense, although I've always used it for these odd patterned ones.
Designers is a vague term used for most any non-normal looking pattern that has been selectively bred for. It may have a more specific use by some, but it is used very generally by most.
For example:
Then you have situations like the first use of the term snow with cal kings. It was used for specimens which were 95% white or so. This was a misuse of the term, since snow is commonly accepted to mean a genotype involving amelanism.
Alot of people do not use the terms exactly as I do, some because they weren't around when the term was first used for something besides what they know it as, and some because they have been around longer than me and remember it as yet another trait.
Part of the problem is the virtual infinite amount of possibilities when it comes to pattern variation. The term aberrant has come to be used for any odd pattern than doesn't fit any of the other common catagories. I think this is best, fewer names is preferred, and all you need is a picture of an aberrant to decide if it's what you are looking for.
There's also several of types that have all but disappeared over the years. Some of these were very interesting looking, but you never see them at all.
The moral of the story is morph definitions vary according to who's using the name, so be sure to get pictures of a cal king before deciding it's what you want.