The Definition of Addiction
The DSM, (Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition) (DSM-IV) says that addiction, or dependence, is present in an individual who demonstrates any combination of four or more of the following symptoms:

Preoccupation with use of the chemical between periods of use.
Using more of the chemical than had been anticipated.
The development of tolerance to the chemical in question.
A characteristic withdrawal syndrome from the chemical.
Use of the chemical to avoid or control withdrawal symptoms.
Repeated efforts to cut back or stop the drug use.
Intoxication at inappropriate times (such as at work), or when withdrawal interferes with daily functioning (such as when hangover makes person too sick to go to work).
A reduction in social, occupational or recreational activities in favor of further substance use.
Continued substance use in spite of the individual having suffered social, emotional, or physical problems related to drug use.

Typically, tolerance is prominent and a withdrawal syndrome frequently occurs when substance use is interrupted. The life of the addict may be dominated by substance use to the virtual exclusion of all other activities and responsibilities. The term addiction also conveys the sense that such substance use has a detrimental effect on society, as well as on the individual; when applied to the use of alcohol, it is equivalent to alcoholism.
Addiction is a term of long-standing and variable usage. It is regarded by many as a discrete disease entity, a debilitating disorder rooted in the pharmacological effects of the drug, which is remorselessly progressive.

The Definition of Substance Abuse
Some people aren’t addicted to drugs or alcohol, but abuse them. The American Psychiatric Association (DSM-IV) definition of substance abuse is at least one of the following four criteria.
Continued use despite social or interpersonal problems.
Repeated use resulting in failure to fulfill obligations at work, school, or home.
Repeated use resulting in physically hazardous situations.
Use resulting in legal problems.

Here is a quote from Terry Kellogg that I really like that hits the nail on the head in my opinion. “Addiction is a pathological,recurring relationship with any mood-altering event, experience, person or thing that causes major life problems. The addiction isn’t because of the substance,experience,person or thing.It is the relationship with the substance that goes awry.There is nothing wrong with banana cream pie, sex or alcohol,the relationship with these is what becomes pathological.”