What is war?
In international law, a war is a legal relationship between states (1). States enter into this relationship when one state declares war on another. Although the specifics vary from law to law, in general war requires that states be using military force to pursue their lawful rights.
Is the War on Drugs a war?
Obviously not. Every part of the definition is untrue:
- It is not a declared war. In the United States, Congress has the power to declare war through a Declaration of War. There is no such declaration for the "War" on Drugs.
- War only exists between two states. There cannot be a war on abstract entities ("drugs", "poverty") or against not-state actors (such as drug cartels). They don't have the international standing to enter into the legal relationship of war.
What about all these other things?
Based on the question and comments made by OP, you are unsure about what to do with other things that seem to be wars: the War on Drugs, the war in Iraq, et cet.
Under the normal view of international relations and international law, these are not wars. So what are they? Why are they different?
A much broader category of international behavior is "armed conflict". Any military conflict fits under armed conflict, even those that aren't war. The Vietnam conflict, war in Iraq, and other military actions are all armed conflicts, but not wars. Armed conflicts do not require any special legal actions, can involve non-state actors, and may include other deviations from ordinary warfare.
Policies like the "war on drugs" and "war on poverty" are only metaphorically wars. They obviously aren't literal wars, but the name suggests we are pursuing them with the same vigor that we would give to a war.
(1) - This is an idea straight from any introductory international relations course. However, this Department of Defense document has a decent non-academic discussion: Law of War (especially starting on page 18).
If you do want an academic article, McNair is one of the classics.