There is not a really big difference in my opinion. I usually think of stores as being bigger, and selling more of a variety of goods. A shop is usually to sell something more specific, and is usually smaller. For example, I would say "grocery store", which usually means a big food market, but smaller stores are sometimes called a "shop".

Store tends to be said more in America. Shop is used more in the UK because you go to a shop to go shopping, and store can also mean to store something, but both make sense.

The buyers of stock are shops, but shop faces to guest . it's just my personal opinion.