Whether your wife cooks from a receipt or from a recipe makes no difference, for today the terms are equivalent in meaning.
Both are derived from the Latin, recipere, “to receive,” the former from the participial form, recepta, the latter from the imperative form, recipe, “take!”
The receipt was originally any set of directions for making up a formulation, whether in cookery or medicine, but in the course of time has pretty well lost its medicinal meaning.
Recipe was used in its literal sense by physicians as the first word in a set of directions for compounding a medicinal preparation (in this sense, now abbreviated), but, because of similarity to the older term, also came to be used as the name for the set of directions, and thence also to a set of directions in cookery.
