They aren't all that different. Alcohol is a drug. All drugs make you feel different in some way because of how they affect your brain -- chemicals in your brain called neurotransmitters. There are a bunch of different neurotransmitters; some make you feel up, some make you feel down. Drugs work by either mimicking neurotransmitters or otherwise disrupting them.
For example, methamphetamine mimics dopamine, a neurotransmitter that makes people feel up, alert, happy. For some people, alcohol also affects dopamine. (If you're the type of person who gets "on" from drinking, rather than relaxed & dopey, that's what's going on with you.)
So your story isn't all that unusual. Plus, once you start using any drug -- alcohol, cigarettes, whatever -- you start interfering w/ your ability to keep your brain chemistry in balance naturally. So you can get yourself started down a path where more and more, you need drugs to make you feel okay. IOW addiction.
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Drugs and Alcohol double duty 
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