Is 売店 more used for smaller stuff, like a stand? I'm finding it hard to pinpoint the exact difference.
You guessed it. 大辞林 has
i.e. a shop selling consumer goods. E.g. a clothes shop:
i.e. a stand selling things. In particular, a small stand/shop in hospitals, theatres, amusement parks or other facilities. E.g. a 売店 in a train station:
In other words, a 商店's main business comes from their goods; a 売店's business comes from their location within some facility.