Psychological dependence is shorthand, used to refer to situations where there is no apparent physical withdrawal, yet there is a compulsion to continue using a substance or carrying out an act. Sex addiction is a good example, as is the compulsion to eat sugar. Psychological dependence is not a medical term.
There is a gray area, and not necessarily a wide one, between psychological dependence and addiction. For example, some heavy users of marijuana suffer withdrawal when they stop using, which qualifies them as addicted. Others have no obvious physical symptoms, but become psychologically disturbed. Also, many activities — gambling, relationships, shopping and so forth — are mood altering and actually create changes in brain chemistry similar to those that occur when we use drugs. Likewise, many activities that we associate with good health, such as running and other forms of exercise, produce changes in the levels of endorphins in our brains, stimulating the very same receptors that are affected by opiates.
As far as treatment is concerned, there is no real difference, apart from the possible need to detox from an addictive substance. We are dealing with the need to change behavior that is causing us problems in our lives, but that we seem unable to stop. The changes we need to make are basically the same, regardless of what we call the circumstances that caused us to seek help.