A pre-approval is a way for hosts to let guests know right away that their space is available to book at the listed rate. Hosts can pre-approve guests in the message thread only after a guest’s initial inquiry. When guests are pre-approved and book within 24 hours, the reservation will automatically be accepted. If 24 hours have passed and they have not booked, they’ll need to submit a reservation request as normal.
It’s important to remember that a pre-approval is not a confirmation of booking. A guest must still click the green Book It button, agree to the terms of the reservation, and submit payment information, after which the reservation’s status will change to “Accepted” in both the host’s and guest’s account.
A Special Offer allows hosts to set a custom price for guests. Guests receive the offer in their message thread and book using the green Book It button associated with the offer. Like a pre-approval, guests can book instantly for 24 hours. After 24 hours have passed, they can still submit a reservation request for the Special Offer price using the green button associated with the offer.
For both pre-approvals and Special Offers, we calculate the Airbnb service fees for you, as normal. If a security deposit is included in the reservation, it is also automatically added.
Here's an example of a Special Offer that is also a pre-approval since it is less than 24 hours old:

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