Fee annulment

I am a very happy Revolut user, but I am wondering about something I couldn’t find any answer yo in the FAQ.

My issue is the following: I checked in a hotel and paid the due fees. Unfortunately, few hours later, the staff at the hotel noticed that they didn’t apply a discount I had, so they asked me to the counter to re-introduce my Revolut card in order to cancel the previous payment, and then pay again the new fees.

I am a little worried because even if I got the receipt that proves that my first payment was canceled, I can’t see the update on the Revolut App.

I am therefore asking: is there any processing difference between a refund and an annulment?
Should I be worried?

Thank you in advance for your answers, and I apologize if my topic is the duplicate of a similar one.