it depends on the country, here in Mexico city we say 'vinatería' for a wine store. Also 'tienda' could be a grocery store. Complete form is 'tienda de abarrotes'.
EVERY SHOP IN SPAIN IS EITHER A TOBAC OR SUPERMARKET they suffer from delusions of grandeur even if it's a wooden shed it's a supermarket. If it's a bodega it's usually owned by BRITS, I SHOULD KNOW I LIVE THERE.
bodega is more of a winecellar type of place, I think it's "tienda" the generic word for small shop, as it is, the Spanish speaking world is a civilised place, where wine and groceries are sold from the same place, and while you're there you can have a sandwich as well