does this mean that neither the giver nor the recipient has to pay taxes on that money?
That is correct. The giver has already paid taxes on the money they have. And someone can receive a GIFT up to a certain amount each year.
“You can give up $12.92 million over your lifetime (tax year 2023) without being subject to gift taxes. This amount increases to $13.61 million for 2024.Oct 5, 2024”