The latter is allowed now - after the backs of the credit card processors were broken.
They fought tooth and nail against cash discounts OR credit surcharges and they finally lost. In some areas it's rampant that you get a pretty substantial discount - often 4 or 5%, better than cash-back - and many places post "cash prices".
You can get even more if you're willing to ride the hassle of the gift card train.
The credit card companies know people spend more if they use credit cards, and they turn around and sell that to the merchants.
The UK actually forbids cash discounts and cred surcharges by law - and has done so since at least 2012.
Credit card companies are allowed to run cashback for using them.
All in the name of "consumer rights": https://www.gov.uk/government/publications/payment-surcharge...
Some European countries forbid a price difference but they also limit card fees very low, so the merchant doesn't lose money and you don't get cash back. Forbidding a price difference but allowing high fees is nothing but pure corruption.
Mainly because cash processing fees are higher than electronic, and the primary use of cash is to avoid paying tax