A cash discount is when you post credit card prices and offer a discount on that price for customers who pay with cash.
The “posted price” refers to prices posted on shelves, menus, or in advertisements.
Compliant cash discount programs must increase the posted price listed on the shelf and then reduce it at the register when customers choose cash.
A surcharge is when you post cash prices and charge an additional fee on top of that price for customers who pay with a Credit Card NOT Debit or Prepaid Card. In the first instance, a customer pays less than the listed price. In the second, they pay more than the listed price.
If you charge more at the register than the listed price, it is a surcharge, regardless of what payment processors call it. Especially if you are being told it’s just a “service fee” or a “non-cash adjustment”, the Card Brands view that as a surcharge.