The difference between these two is that the first blames minorities for doing badly in education and the second blames the mainstream, white-dominated culture.
The deficiency explanation focuses on the perceived shortcomings of minorities. It argues that there is something wrong with the minorities themselves that makes them less able to achieve. This used to be blamed on genetic inferiority but such theories now tend to focus on alleged cultural deficiencies.
By contrast, the cultural bias explanation blames the dominant culture. It argues that the US educational system is set up in ways that disadvantage minorities. The theory says, with the system biased against them, it is no wonder that they do not achieve at the same levels as whites do.