They're really not that closely related. A "privilege" is only a noun (the related adjective is "privileged.") It means a special advantage that's granted by some authority to a specific person or group, as opposed to a "right" which is intrinsically available to a certain group or to all. "Differential" can be an adjective or a noun, and it's much more general. As an adjective it's closely related to "different", and as a noun it's usually closely related to "difference." The noun also has other more specific meanings in fields like medicine or car engines.

We need more context. Both words have a variety of meanings and usages. "Differential" is very closely related to "difference." It sometimes just means "difference." It sometimes means "difference where there shouldn't be any;" a difference in comparable things. For example, there's a wage differential between men and women doing the same job. My guess is that's your meaning. "Privilege" means "something that entitles you to special rights or extra benefits." It might be deserved--"the employee of the month has the privilege of parking in a closer parking space." It might be undeserved. In the context of a social hierarchy, if two people, A, and B, have a differential in some kind of status--person A gets a four-drawer desk while person B only gets a three-drawer desk--it might be evidence that person A belongs to a privileged group.

What is the context? They seem to be two completely unrelated words... but maybe in a particular context they have some similar meaning?