There is absolutely no difference in the law as to whether you are under the influence of alcohol or weed, or any other substance (legal or illegal) that impairs your ability to drive.
DUI is just that DUI, it does not distinguish or change punishment based on what substance you are Under the Influence of.
There is a DUI and a DWI.
Compare to instances: 1. A person kills someone while driving a car while sober. 2. A person kills someone while driving a car while not sober. Which one gets more punishment?