Liquor for off-premises consumption can be sold in some states only in state-run stores; in other states in privately-owned stores (which stores may, or may not, also sell beer and/or wine, depending on their location); or, in some states, grocery stores.
Differing laws apply to wine or beer for off-premises consumption -- where they may be sold, and when (Sunday sales banned in some jurisdictions; Sunday sales only after 11 AM or Noon or 1 PM in others).
Laws pertaining to on-premises alcohol are even more perplexing. It is commonplace for a totally "dry" county to be adjacent to one which allows bars as well as off-premises sales. There have been counties where you can buy a bottle of bourbon from a state-run store, but not a drop of beer may legally be sold. And so on -- every imaginable permutation of what kinds of adult beverages you may buy, from whom, and under what circumstances.
I live in Union County, NC, on the southeastern fringe of the Charlotte metro area. It is legal for towns within Union County to permit the establishment of state-run liquor stores, if approved by a majority of voters in a referendum -- if, that is, the state Alcoholic Beverage Commission thinks it can sell enough liquor at the location in question to make it economically justifiable. Sales of beer and/or wine by private stores (grocery stores, convenience stores, gas stations), similarly, are subject to the passing of a referendum. And ditto for the establishment of bars, within the rather tight NC laws (establishments must derive 50% or more of their revenue from food, and, significantly, must buy their liquor from state-run warehouses, not at wholesale, but at retail plus a surcharge, which theoretically goes to programs to prevent alcoholism).
Again, all of this is subject to voter referendum, on separate questions; some towns have approved beer and wine sales by groceries, but turned down state liquor stores and/or liquor licenses for restaurants. Unincorporated areas of Union County are totally dry. The effect of that has been that there are no grocery stores in the county other than in towns which have approved sales of beer and wine in grocery stores.
In an ultimate irony, Lynchburg, Tennessee is in a dry county.