How are alcoholism and drug addiction different?

Not a lot different: Clearly different substances can have different effects or intoxicated states or damage the body in different ways. However to get better from any substance problem be it alcohol or Cocaine much of the same treatment in employed, at the end of the day people with substance abuse problems need to learn how to cope with life or they relapse on their drug of choice. Rehabs accept all comers.

Choice of addiction: Addicts have choice of drugs they use for addiction- alcohol or drugs.

They are not: The main difference is that alcohol is legal and easier to get. Because it is legal and socially tolerated, alcohol can be abused longer before accumulating the consequences associated with addiction to illegal drugs. There appears to be a link between alcoholism and opioid addiction; one of the drugs used to reduce alcohol cravings blocks opioid receptors.