Caterpay is a payment gateway, just like your PDQ machine.
Your PDQ machine uses a Merchant ID (a "MID") from a acquiring bank which is for face-to-face or "customer present" transactions (ie the hotel guest enters their PIN on the terminal and this is used as the authentication).
Caterpay needs a MID that is configured for customer NOT present transactions. You don't see the guest when they offer their card details, as often they will be at home or work making the booking online or over the phone. They authenticate themselves using the CVV number (web and phone) and sometimes using a Verified by Visa or Mastercard 3D Secure password on your website.
Transactions charged through your PDQ machine take up to 3-5 working days to be processed by the banking system and are then "settled" into your business bank account.
In exactly the same way, transactions charged through your Caterpay will also take up to 3-5 working days to be processed by the banking system and are then "settled" into your business bank account.
In practice, most transactions are settled overnight these days.
Before going live with Caterpay, we strongly recommend making a test transaction of a low value, eg £1.01 using your own card. You should keep an eye on your business bank account for that amount being deposited 3-5 days later.