Yes, in most setups the money your customers pay goes straight into your own bank account. Your portal is connected to a payment gateway that is opened in your own business name, so the card payment is processed as a payment to you rather than to anyone else. Your customer sees your brand at checkout, and the charge on their card statement reads as your business.
The way it usually works is that you apply for a merchant account with a payment gateway or with your own bank, they approve you, and then those details are added to your portal. From that point, every online booking is charged through that gateway and settled into your account on whatever timetable the gateway gives you. We do not sit in the middle holding your funds.
There are a few honest limits worth knowing. Not every gateway can be connected, so it depends on which ones are supported in your country and on the plan you are on, and the gateway itself decides whether to approve your business. Card fees, refunds and chargebacks stay a matter between you and your gateway. Separately, many airline and hotel suppliers still need to be paid from a deposit or credit account you hold with them, so customer money arrives with you while you fund the supplier yourself.
Before you commit, ask your bank or your preferred gateway what sort of merchant account you can get, and check with us that the gateway you have in mind can be connected to your portal.