Graft:
Graft is a form of political corruption in which an official acquires financial gain by dishonest or unfair means, especially through the abuse of one’s position. Unlike bribery, graft does not require the official to provide an undue advantage; it is enough that she/he gains something of value apart from her/his official pay when working.
Patronage:
Patronage is a system in which a number of organizations, companies and/or individuals bestow support or financial benefits upon one another. Political patronage occurs when political supporters are rewarded for their support (e.g., by being appointed to public office or receiving contracts, subsidies or other benefits), regardless of merits.