The first of these terms should be related to defect, the second to deficit. For example, money that is counterfeit is defective because of its defect. Money is deficient if there is not enough of it. Defect is the general word for any kind of imperfection or shortcoming; deficit is the general word for "shortage" or "lack." Thus one might refer to a child as being "mentally deficient" ("lacking normal intelligence") and "physically defective" ("imperfect in hearing or speech").
Dictionary of problem words and expressions. Harry Shaw. 1975.