I have a problem with smoking in public places where there are children
Restaurants are NOT public places, they are private establishments that INVITE the public into them.
Public places are places that nearly everyone is required to go at some time (DMV, courts, etc) and are payed for with tax dollars. No one is ever required to go to a bar or restaurant.
And even employees are not required to go where they don't like the atmosphere, because they are not required to have taken a job where they do not like the atmosphere.
Your definitions of bars and restaurants and the purposes they serve are correct, to a point. And may very well be exactly on point for California, but not everywhere.
Here in Delaware bars are not permitted to be open on Sunday, but restaurants are. There is not a "sports bar" in the entire state that does not hold a restaurant license.
Everyone of them has a full kitchen and a full menu - but the primary business is bar business, particularly on the weekends for football and NASCAR. Because they have a restaurant license they must admit those under 21, including little children - something most of them discourage.
Because Delaware is such a small state - maximum drive to another state is 35 miles, those places in particular have been hit very hard with the Delaware smoking ban.