There is an important distinction between being "sober" and being in "recovery". The differences are clear to those who have experienced both phases in their healing process from alcoholism.
When an alcoholic is "sober" from alcohol without attending a mutual-help program, therapy, medication management and/or treatment then they are in a sense "white knuckling" their sobriety (also referred to as being a "dry drunk"). These individuals may be staying away from alcohol, but they are not treating the underlying issues that had either led to their drinking in the first place or developed as their alcoholism progressed. Many "sober" alcoholics who are not in "recovery" will experience a transfer of addictions that could involve a new addiction to food, sex, shopping, romantic relationships, etc. because they have not found a healthy way to fill the void that alcohol had satisfied. They may have stopped drinking, but their life may be exactly the same, leading them to be jealous of others who are drinking or to struggle with emotional or mental health issues.
An alcoholic who is in "recovery" is essentially in remission from alcoholism. Their alcoholism is not cured, but is at bay in a way that allows them to be free of the cravings, mental obsession and they have treated their underlying issues (mental health, spiritual, physical) that led to or resulted from their drinking. These alcoholics have found a way to fill the void once satisfied by alcohol through spiritual, emotional and/or behavioral solutions that they have learned through treatment, therapy, medication management and/or mutual help groups (A.A., SMART Recovery). They have made significant changes that have allowed them to find peace in removing alcohol from their life and to have emotional stability.