YEs, exposure should be in your mode, then adjustment covariates such as age and maybe gender, and then nuisance factors (confounders). I wouldn't get formal with these terms, since they really amount to study factors and nusaince factors. You should try to get rid of confounders and show that odds ratio of the risk factor (E) is not altered significantly by the confounder(s). Confounders are basically problem (nuisance), so you would rather not deal with them. However, confounders in your study would be variables significantly different between drinkers and non-drinkers that are not your exposure variable.