Receipt, recipe, prescription are comparable when they mean a formula or set of directions for the compounding of ingredients especially in cookery and medicine.
Receipt is often employed as a designation of a formula for making a homemade medicine. Though also often used in reference to cookery formulas, the term in this sense is commonly felt as old-fashioned or dialectal and is being gradually displaced by recipe.
Recipe is perhaps the most general of these terms since it can apply not only to a formula or set of instructions for making or doing something but to a method or procedure for attaining some end.
In application to medicinal formulas recipe may come close to receipt or it may suggest an old-fashioned empirical remedy as distinct from a modern pharmaceutical product.
In cookery recipe is the usual and standard English term for a set of directions for preparing a made dish.
The usual term for a physician’s direction to a pharmacist for the compounding or dispensing of a medicine is prescription. That term is also applied to a medicine which is compounded or dispensed according to such a direction.