A shop is small and is often where something is MADE.
candy shop
book shop
flower shop
liquor shop
ice cream shop
coffee shop
Some of these places USED to make things but now they don't... so shop and store are both often used. I think it depends more on where you are from. For example, in Montreal I am more likely to say liquor store but when I visited the US I often heard liquor shop.
Stores are usually larger.
candy store
shoe store
liquor store
book store
BUT I've never heard coffee store(it would be a place that sells coffee BEANS only and no drinks) or flower store(because they MAKE bouquets at a SHOP). Or ice cream store because they MAKE our ice cream cone and serve it to us.
A bar is a place with a counter.
So it is usually somewhere that serves drinks... like a bar~! But you might also hear coffee bar, sushi bar, oxygen bar, etc.
I hope that helps clear things up~!
Phil