The stigma is associated with the perception of a lifestyle that is somewhat unacceptable. People who drink are often portrayed as irresponsible degenerates who take their lives and the lives of thers in their own hands by driving drunk when the behavior could be avoided entirely. There is very little mystery about it. If someone slugs five shots of yeagher and gets behind the wheel to drive, they have made a decision to disregard the danger to others on the road. If someone gets a phone call while driving, the deicions to pick the call or respond is more of a reaction than a plan. There is a difference in perception. Which by the way is what stigma is. Perception. MANY people who have drunk driving accidents actually slow down the drinking or are borderline over the limit and make what they believe is a decision not to drive drunk. Also, and this is important, many drunk driving accidents have someone impaired who is driving, but the casue of the accident is not drunk driving. And please note that distracted driving...texting, etc...is starting to carry its own stigma. And stiffer penalties.
Society responds to what it percieves to be society's evils. Driving drunk has taken the lives of millions of people around the world since driving began. There are generations of people who can point to incidents that go back that far. Drunk driving has had the time to earn its place as the number one killer of young people. A drunk driver is stigmatized, rightfully or not...for the sins of those who went before him or her.
Final shot on smoking. A huge tobacco lobby has some control over the advertising and presentation of the product. The people who smoke may or may not have an affect on those who do not. It's also easy for a smoker to say "well, it wasn't MY smoking that caused damage to that third party." And they would probably be right in most cases. The nexus between smoking and inuries to others is not as clearly defined.
As for other activities while driving, again, most of those are just in the normal course of living. Talking, turning your head to see something, even the act of driving carefully requires you to move your attention from one place to another. Things that caiuse accidents as a result are the reason we use the word accident. That's just what they are.
Over the years, I have lost a considerable number of friends and family to accidents of all kinds. I never really much cared about stignma. There have been people who caused accidents who were drunk. Some who were not. I don't remember feeling very forgiving for them one way or another.