Here, we will consider the definition of “addiction”, and compare it to the criteria used for the definition of “obsession”. According to the American Psychological Association, addiction can be defined as a brain disease that is manifested by compulsive substance use despite harmful consequences. People with addiction (severe substance use disorder) have an intense focus on using a certain substance(s), such as alcohol or drugs, to the point that it takes over their life. They keep using alcohol or a drug even when they know it will cause problems.
The DSM-5 uses two criteria to define obsessions. First, recurrent and persistent thoughts urges, or images that are experienced, at some time during the disturbance, as intrusive, unwanted, and that in most individuals cause marked anxiety or distress. And, second, the individual attempts to ignore or suppress such thoughts, urges, or images, or to neutralize them with some thought or action (i.e., by performing a compulsion).
I hope this helped you understand the difference between addiction & obsession.