Is there a difference between a codeine and morphine addiction?

Not a bit: Codeine has almost no analgesic activity in most people. After it is absorbed by the gut, the Codeine dissolved in blood passes through the liver wherre an enzyme converts it to morphine! some people (usually asian) lack this enzyme and get no effect from Codeine (except constipation). Morphine is available in larger dose pills, so, its easier to get dependant on higher doses.

A little: Codeine tolerance rarely gets as high as other opioids. Otherwise, no difference.