Hibah (هبة) is a gift (an amount of wealth) given gratis (for no consideration/ iwadh) for the sake of the recipient. In the case of hibah, the giver (wahib) usually knows the identity of the recipient (mawhoob lahu) and there is a direct interaction (and maybe previous acquaintance) between them.

Hadiyyah (هدية) is also a gift or present but one that is associated with cordial affection, appreciation and gratitude, or admiration towards the recipient. It may be extended in return for a favor or in goodwill. In this sense, hadiyyah is a specific form of hibah (it is usually personal and harbors specific feelings, wishes, etc.)