drug abuse
Definitions:
1. habitual use of drugs not needed for therapeutic purposes, solely to alter one's mood, affect, or state of consciousness, or to affect a body function unnecessarily (as in laxative abuse).
и тут
https://www.addictioncenter.com/addiction/addiction-vs-depen...
The difference between addiction and dependence can be difficult to understand.
When people use the term “dependence,” they are usually referring to a physical dependence on a substance. Dependence is characterized by the symptoms of tolerance and withdrawal. While it is possible to have a physical dependence without being addicted, addiction is usually right around the corner.
Addiction is marked by a change in behavior caused by the biochemical changes in the brain after continued substance abuse. Substance use becomes the main priority of the addict, regardless of the harm they may cause to themselves or others. An addiction causes people to act irrationally when they don’t have the substance they are addicted to in their system.
Addiction encompasses both a mental and physical reliance on a given substance

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Note added at 13 mins (2016-03-28 14:44:40 GMT)
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Зависимость, конечно.

https://www.drugabuse.gov/publications/principles-drug-addic...

Считаю, что так. Вариант Марка Рабкина тоже, в принципе, неплохой, только слово "пристрастие" не такое однозначное как "наркозависимость", т.к. имеет более широкое значение. Можно говорить о пристрастии к курению, азартным играм и пр.

"Наркозависимость" - более однозначный термин, когда речь идет о лекарственном средстве.

Подробно о разнице м/у addition and dependence (хотя перед dependence нет слова physical, думаю, оно здесь подразумевается):
http://www.naabt.org/addiction_physical-dependence.cfm/

Physical dependence can occur without addiction; this is the common experience of most chronic pain patients who are able to take their opioid medication as prescribed for pain but don't develop the uncontrollable compulsion and loss of control. A desire to avoid withdrawal is not addiction.

Addiction can occur without physical dependence; consider cocaine or methamphetamine both have little outwardly apparent withdrawal syndrome but addiction to either can devastate lives. Non-substance addictions such as gambling, sex or internet also have no physical dependence. What is common to all these addictions is the unnatural cravings that prompt the compulsive behaviors.

Physical dependence is sometimes simply called dependence, but this can lead to confusion because addiction is sometimes called dependence as well.