The words addiction and obsession can appear to describe the same thing. And yet there is a clear distinction between the two. An obsession is something that is usually in the mind and can relate to people, things and ideas; so all that is abstract and all that is concrete.
On the other hand, an addiction is something that could be described as a doing and relates to the actions that one takes. It is possible for one to be addicted to something without thinking about it all the time; and for someone to be obsessed by something without the need to act on the obsession.