Question: Lets say I buy something at some (physical) store and pay using a credit card on one of these electronic terminals. What information do the owners of this store get about me (or my credit card) from this transaction?

Can they find out whether multiple purchases were paid using the same credit card?

Answer: 
At the very least, they can get the card number. Most receipts will even have the last few digits of the card number printed on them, but the system will have had the full number at some point, and may well hold a tokenised version of the card number which is allowed under PCI (think of it being a random value which can be linked back to the card number by the tokenising service). Since the same card probably gives the same token each time (technically this is optional, but since it gives more information than the alternative, it's the more common in practice), they can go "this card also bought X, Y and Z on these dates".

They can't usually cross reference that data with other stores though - the token associated with a given card from store A is completely unrelated to that associated with a given card from store B, in a sensibly designed system. I don't know whether any tokenisation providers pool data from multiple clients, but that could be a potential nightmare under GDPR, so I'd assume not, at least in Europe.

The issuing bank can also see purchases being made, obviously, but usually in a per transaction basis, rather than individual items. That doesn't mean they can't make educated guesses about the purchases (e.g. if you make a payment to a business called "99p Donuts" for 99p, it's a pretty safe guess that you bought a donut...),
Just to add to the previous answers: Apart from the obvious data that is entered during checkout, you can also get the issuing bank name from the first 6 numbers of the credit card number. With the bank name you can sometimes guess the country where the card was issued when you get a result like "Bank of China", "ANZ" or "Národná banka Slovenska".

I used this method (along with others) in an online store when calculating a risk factor before an order was shipped, to eliminate or flag orders that are placed with stolen credit card numbers. 
If user IP, delivery address and bank card are all from different countries then your order would go on hold and flagged for manual review.