Depends on context. If you're discussing it in a medical context, the terms are separate. Dependence refers specifically to the severity of the effects of stopping the drug, both physical and psychological. Addiction is more about the behavior of a person when exposed to the substances and is not as strictly defined of a term in a medical sense. But generally, dependence is a component addiction. So not all dependence results from addiction, but most definitions of addiction include some kind of dependence.

So, not the same thing, but also, outside of medical context, most people don't differentiate the terms and use the word addiction to refer to the dependence component of addiction.