I think you may be confusing actual Booking Requests with mere Pre-Approval inquiries.
A pre-approval inquiry comes from a potential guest who hasn't fully decided that they want to book. They may send inquiries to multiple hosts but those inquiries don't commit the guest to anything. As a host, you're given the option of pre-approving the guest or declining to pre-approve. If you pre-approve, the guest has 24 hours to book (without further approval from you) before your approval expires. During that time, your listing isn't blocked and you can, in fact, accept any other booking request or pre-approval request.
A Booking request doesn't arrive to you with a pre-approve option. Instead, you can either Accept the booking or Decline it. By making a Booking request instead of a pre-approval inquiry, the potential guest has made a commitment to you and to AirBnB. If you approve the booking, they're booked. At that time, they owe AirBnB their service fee, and depending on your chosen cancellation policy, they're committed to paying you for their stay (if they stay) or all or part of it (or even none of it) should they cancel by certain dates.
AirBnB's "Help" center has lots more about all of this. I suggest looking there first when you have questions. For example, here are *their* words about Pre-Approvals:
https://www.airbnb.com/help/article/838/what-is-a-pre-approval