Hibah (هبة) is a gift (an amount of wealth) given gratis (for no consideration) 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.

Sadaqah (صدقة) is an amount of wealth given for the sake of Allah, not to solicit any commendation or reward from the recipient. In the situation of sadaqah (alms), the giver (mutasaddiq) usually does not reveal his/her identity to the recipient of sadaqah and need not know- and never seeks to know- the identity of the recipient (usually there is no personal relationship involved).