Abstinence from both is required for recovery
As far as the biochemistry of your brain that is related to addiction is concerned, there is no difference among drugs. They affect the brain's neural pathways in somewhat different ways, but the end result is the same: craving when the drug is withdrawn.
The only way for the brain to repair itself is to withdraw all drugs, including alcohol and weed, and allow it to recover. This can take up to a couple of years, especially in the case of opioid drugs, and is the period after acute withdrawal that we call PAWS. Further drug use will reactivate the addiction pathways, and will likely lead to a renewal of the addiction.
Especially during early recovery, replacement addictions are common. These may include gambling, sex, thrill-seeking, and a variety of other substitutes. The key is compulsion. If you feel as though you have to do those things in order to feel okay, the likelihood is that you are developing or feeding another addiction. These things will crop up. They do for all of us. They involved the pleasure centers of the brain, same as addiction, which are starved for stimulation in early recovery. The trick is to recognize them, admit them, and use your program in NA or AA to help get past it.
Recovery isn't for sissies. Good luck, and keep on keepin' on!
Bill