Having e.g. a system for booking flights, during UAT it is not being tested by real users (customers who will buy tickets) rather than people from the client side who will just simulate this. Are there any more specific terms to distinquish between real users (like end user) and users doing the UAT?
The customers who are going to buy ticket are not the real users of the application.
Real users are those who are going to deploy the application and will be operating the system.
Customers will just be requesting for the ticket, mentioning their details (not filling any of the details at their own). The employees of the company will be operating the application, filling the details mentioned by the customer and filling other requirements.
So, the employees will be the real users. They participate in testing, as they need to customize the application as per their requirements.
The distinction doesn't matter. Your acceptance testing should encompass all of the functionality that is exposed to the end user. You absolutely should test it as if you were the end user, as well as testing edge cases and unusual scenarios that may only affect a handful of end users.
Where I work, we are building an internal application and use the terms 'the business' (which are the real end users) and 'testers' (those who do the UATs).