Uh, if by 'government run' store you mean stand alone alcohol store, then yes. Here in GA it varies by county if liquor is even sold. Beer and wine is sold all over the state and you can buy that from the grocery store to a gas station. Liquor in most counties requires a separate store specifically for the purpose of selling alcohol.
Yeah ok. Well here if it contains any alcohol at all you can't sell it outside a government licenced store. Either run directly by the government or a store with a licence to sell alcohol and NOTHING else. This includes all beer and wine. You won't find regular beer or wine in any corner store or grocery store.
Typical liquor stores look something like this:
Similar in concept I think to the state run stores you have only it's stricter because you can't get alcohol outside these types of stores at all in any form beer wine or otherwise.
EDIT: Licenced restaurants serve alcohol like anywhere else of course.