The shop can correlate all of your purchases (down to individual items) into a single purchaser profile tied to your credit card number -- basically the same as if you used a loyalty card with all of your purchases. If they can ever gain the ability to link a credit card with an identity, (say, via a credit card purchase that uses your loyalty card) then they can link multiple credit card profiles together.
In terms of data flow, it mostly goes the other way. It allows the shops to sell this data about you to others. Your credit card company does this, of course, but the only "direct" visibility they get is to the establishment. "In an average month, _trampeltier spends $x at grocery stores, $y at liquor stores, $z at tobacco shops", etc. They don't learn the actual itemized purchases without cooperation from shops (who of course have this data). Though I wouldn't be surprised if that was built into credit card processing agreements at this point, who knows.
In terms of data flow, it mostly goes the other way. It allows the shops to sell this data about you to others. Your credit card company does this, of course, but the only "direct" visibility they get is to the establishment. "In an average month, _trampeltier spends $x at grocery stores, $y at liquor stores, $z at tobacco shops", etc. They don't learn the actual itemized purchases without cooperation from shops (who of course have this data). Though I wouldn't be surprised if that was built into credit card processing agreements at this point, who knows.