A gift of equity is a home sale in which the seller deliberately accepts less than the home's fair market value, and the difference between the value and the price is treated as a gift to the buyer that the buyer can use toward the purchase. Fannie Mae's Selling Guide defines it as "a gift provided by the seller of a property to the buyer," which "represents a portion of the seller's equity in the property, and is transferred to the buyer as a credit in the transaction." Fannie Mae accepts it only from a seller who meets its personal-gift rules for donors, which makes it a transaction between relatives or people with a family-like relationship.
The same transaction is looked at three ways at once: by the lender, as a source of the down payment; by the IRS, as a part-sale, part-gift; and by the two parties' future tax returns, through the seller's gain and the buyer's basis. Each of those has its own rule, and the rules do not all point the same way.