Brand equity is a financial calculation. It is the difference between a commodity product or service and a branded one. For example if you sell a plain orange for $.50 but a Sunkist orange for $.75 and the Sunkist orange has brand equity you can calculate it at $.25 per orange.
Brand parity exists when two different brands have a relatively equal value. The reason we call it "parity" is that the basis of their value may be different. For example, one brand may be seen as higher in quality, while the other is perceived as fashionable.