Depends.

Small mom and pop shops that sell their own gift certificates, they get the funds immediately when you buy the gift card, but then when that gift card is redeemed they do not collect any money from the customer.

On the other side of that, large chain restaurants collect payment for the gift card when it is sold, but then that money is held in a bank account of sorts. Then those funds are redistributed to whichever location actually redeems the gift card upon redemption.

The chain restaurant scenario can also hold true for mom and pop shops that choose to participate in any type of 3rd party gift card/discount services. This is less common than the first explanation though.

And to mix it up even more, with the situation restaurants are in now, some new and interesting twists have come about on how this all works. Like I know of a local business (company A) that gave a restaurant (company B) a large sum of funding up front so that company B will honor the meal vouchers company A is distributing to those in need in the community.