Often when people, and especially the media, say "addiction" they're actually referring to psychological dependence.
Most physiological addictions have a psychological component. As an example, I'm addicted to caffeine, but I'm also dependent on coffee as part of a morning routine. Smokers who are addicted to nicotine are often also dependent on the social aspects of being a smoker. It's often the psychological component that, long term, is the hardest to break.
The converse, however, is not true. A good example is so-called "Internet addiction" which should rightfully be called "Internet dependence", at best, because it has no physiological component.
To say that something like internet addiction has no physiological component is to vastly understate the power our brain has over the rest of our body. If your method of getting a dopamine rush is the internet (or world of warcraft, porn, gambling, etc), you are still going to get physiologically attached to that dopamine rush and will suffer negative physical reactions (poor mood, etc) if those things are taken away.
There is a difference between using something (and getting used to it because it increases your quality of life) and a chemical addiction.
> The chemical/psychological distinction is hardly important.
There is a huge difference. If you are addicted to something it is pretty much a physiological effect on you.