I did some research comparing the two different kinds of snakes. My research is showed below. Everything highlighted is cited and everything not cited is from my own experience and handling snakes myself.
Adult corn snakes need a cage at least the size of a 20-gallon long aquarium, but bigger is even better. Snakes are not social animals, so cage-mates are quite stressful. House only one corn snake to a cage. Climbing branches may be appreciated, but a couple of dark, tight hides are essential to help the snake feel secure.
A general rule is that if the snake crawls around the perimeter of the cage and doesn't cover more than 2/3 of the distance, the cage is large enough – but bigger is better. An adult California king snake requires a 20-gallon or larger enclosure.
From experience 2 things. Don't keep two snakes in the same cage because it can be stressful with the other snake because they aren't social animals. Snakes have been known to be cannibals to other snakes so having 2 snakes in the same cage isn't a good idea. 2nd thing is that your habitat for the snake has to be secure. If a snake can find a weak spot before you can, then the snake can get out and potentially cause problems depending on the snake. But I don't think that people would want snakes running around their house.
Most breeders use aspen shavings as bedding because it is absorbent, soft and holds its shape when snakes burrow. Cypress mulch also works, but avoid aromatic woods such as pine or cedar. Newspaper and reptile carpet also suffice, but the corn snake tends to get under it whenever possible. Avoid sand because it may cause impactions if ingested.
King Snake Substrate
Many commercial substrates and beddings for reptiles are available. Avoid cat litter and any chemically treated substrates and oily woods. General rule, if it looks good and doesn't give off a smell, it is OK. Feed your California king snake in a separate container if the substrate could be ingested while feeding. Newspaper, paper towels and indoor carpet are fine, but if the snake can't partially burrow in your substrate, you might consider a hide or two in the cage for security.
The primary natural food of corn snakes is appropriately sized rodents. Adult corn snakes may eat birds or their eggs. Do not offer crickets because corn snakes don’t recognize them as food.
Food King Snake
In captivity they should be fed rodents, usually mice, which are readily available. You can offer live or well-thawed frozen mice. Live adult mice can inflict wounds to your king snake. Fresh killed is a safer choice.
Temperature for a King Snake
California kingsnakes require no special lighting if the cage is in a room with natural light. Be sure not to place the cage in or near a window where the sun will shine on the cage, or it can become too hot and fatal for your king snake.
In captivity, choices are limited to what you provide so you should have a warm end and a cool end of your cage.
Try to achieve 85 degrees Fahrenheit at one end and in the 70s at the cool end. Do not use "hot rocks," the heat is too centralized and can cause burns.
Temperature for a Corn Snake
Provide a temperature gradient with a light, or undertank heat pad or cable. On the warm end 85 degrees Fahrenheit is perfect, and room temperatures (low 70s) are fine for the cool end. One long, skinny hide, such as a hollow log or PVC pipe, can be placed so one end of the hide is cool and one end is warm. Be sure to check the temperature inside the warm end of the hide — not on the glass. Temperatures can vary quite a bit within just a few inches, so thermometer and hide box placement is important.
Always for both snakes feed them at least every 7 to 10 days. If your snake is an adult avoid feeding it too much because it can cause obesity.
In the end the only difference is the difference in Caging Substrate and food but the food items to the snake can blend in because you can feed both rodents.
All citations are under the link: http://www.reptilesmagazine.com/Care-Sheets/Snakes/