Alcoholic and workaholic are not the same. They are far from being the same. The only similarity is that these terms are used to refer to addiction to something. An alcoholic is an individual that is addicted to the use of alcohol. Such a person abuses the use of alcohol.
The term can also refer to the trace amount of alcohol in content. On the other hand, a workaholic is an individual who feels compelled to work excessively. A workaholic puts his or her work above every other thing. Their family, friendships, relationships, and other parts of their life suffer at the expense of their work.